diff --git a/libraries/AP_Motors/AP_MotorsMulticopter.cpp b/libraries/AP_Motors/AP_MotorsMulticopter.cpp
index ed83503a77..7789a65f68 100644
--- a/libraries/AP_Motors/AP_MotorsMulticopter.cpp
+++ b/libraries/AP_Motors/AP_MotorsMulticopter.cpp
@@ -116,6 +116,14 @@ const AP_Param::GroupInfo AP_MotorsMulticopter::var_info[] = {
     // @User: Advanced
     AP_GROUPINFO("SPIN_ARM", 19, AP_MotorsMulticopter, _spin_arm, AP_MOTORS_SPIN_ARM_DEFAULT),
 
+    // @Param: BAT_CURR_TC
+    // @DisplayName: Motor Current Max Time Constant
+    // @Description: Time constant used to limit the maximum current
+    // @Range: 0 10
+    // @Units: Seconds
+    // @User: Advanced
+    AP_GROUPINFO("BAT_CURR_TC", 20, AP_MotorsMulticopter, _batt_current_time_constant, AP_MOTORS_BAT_CURR_TC_DEFAULT),
+
     // @Param: THST_HOVER
     // @DisplayName: Thrust Hover Value
     // @Description: Motor thrust needed to hover expressed as a number from 0 to 1
@@ -207,7 +215,6 @@ void AP_MotorsMulticopter::update_throttle_filter()
 }
 
 // return current_limit as a number from 0 ~ 1 in the range throttle_min to throttle_max
-//todo: replace this with a variable P term
 float AP_MotorsMulticopter::get_current_limit_max_throttle()
 {
     // return maximum if current limiting is disabled
@@ -224,7 +231,8 @@ float AP_MotorsMulticopter::get_current_limit_max_throttle()
 
     float batt_current_ratio = _batt_current/_batt_current_max;
 
-    _throttle_limit += AP_MOTORS_CURRENT_LIMIT_P*(1.0f - batt_current_ratio)/_loop_rate;
+    float loop_interval = 1.0f/_loop_rate;
+    _throttle_limit += (loop_interval/(loop_interval+_batt_current_time_constant))*(1.0f - batt_current_ratio);
 
     // throttle limit drops to 20% between hover and full throttle
     _throttle_limit = constrain_float(_throttle_limit, 0.2f, 1.0f);
diff --git a/libraries/AP_Motors/AP_MotorsMulticopter.h b/libraries/AP_Motors/AP_MotorsMulticopter.h
index 53a9f3879a..b94649b1e9 100644
--- a/libraries/AP_Motors/AP_MotorsMulticopter.h
+++ b/libraries/AP_Motors/AP_MotorsMulticopter.h
@@ -23,7 +23,7 @@
 #define AP_MOTORS_BAT_VOLT_MAX_DEFAULT  0.0f    // voltage limiting max default
 #define AP_MOTORS_BAT_VOLT_MIN_DEFAULT  0.0f    // voltage limiting min default (voltage dropping below this level will have no effect)
 #define AP_MOTORS_BAT_CURR_MAX_DEFAULT  0.0f    // current limiting max default
-#define AP_MOTORS_CURRENT_LIMIT_P       0.2f    // replace with parameter - Sets the current limit P term
+#define AP_MOTORS_BAT_CURR_TC_DEFAULT   5.0f    // Time constant used to limit the maximum current
 #define AP_MOTORS_BATT_VOLT_FILT_HZ     0.5f    // battery voltage filtered at 0.5hz
 
 // spool definition
@@ -153,6 +153,7 @@ protected:
     AP_Float            _batt_voltage_max;      // maximum voltage used to scale lift
     AP_Float            _batt_voltage_min;      // minimum voltage used to scale lift
     AP_Float            _batt_current_max;      // current over which maximum throttle is limited
+    AP_Float            _batt_current_time_constant;    // Time constant used to limit the maximum current
     AP_Int16            _pwm_min;               // minimum PWM value that will ever be output to the motors (if 0, vehicle's throttle input channel's min pwm used)
     AP_Int16            _pwm_max;               // maximum PWM value that will ever be output to the motors (if 0, vehicle's throttle input channel's max pwm used)
     AP_Float            _throttle_hover;        // estimated throttle required to hover throttle in the range 0 ~ 1