In order to solve the overshoot problem of acceleration tracking due to inaccurate model when tracking maneuvering targets with cubature Kalman filter, we made study on the square root filter and memory attenuation filter, and proposed a square-root cubature Kalman filter improved by memory attenuation factor, i. e. , Memory Attenuation Square-root Cubature Kalman Filter(MASCKF). Firstly, a simplified square-root cubature Kalman filter based on linear state equation was deduced for improving the real-time performance of the algorithm. Then, memory attenuation factor was applied to the link of time updating of the simplified algorithm. Therefore, the weight of new measurement data was increased during the estimation, and the overshoot of acceleration tracking was well suppressed. Experimental results demonstrate the effect of the new algorithm on overshoot suppression, which can improve the accuracy and real-time performance of target tracking.