The mixing operation which is a key component in interacting multiple model(IMM) filter yields a non-Gaussian probability density function(PDF), IMM approximates the PDF of mixed random variable by a single Gaussian, the estimated covariance matrix is much large than the real covariance. As the mixing probability is time-varying, the mixing operation can be described as a nonlinear function, then the cubature rule in cubature Kalman filter(CKF) can be used to compute probability density function(PDF) of the mixture, that algorithm is called cubature rule aided interacting multiple model(CRIMM) filter. The accuracy of the resulting mean and covariance are analyzed by Taylor expansion. Simulation results show the CR-IMM performs better than IMM when the measurement becomes less accurate.