In this paper, a statistically robust precoder design for space-time coded amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay networks over double-correlated Rician fading channels is presented. In this network, the source, destination, and relay nodes are equipped with multiple-antenna. The precoder design is based on channel means and covariance matrices for the sake of reducing channel feedback. Since the average received signal-to-noise ratio (SNR) is closely related to the bit error rate (BER), it is adopted as an objective function. Unfortunately, this objective function is difficult to obtain a simple expression. An accurate approximation of a lower bound of the average received SNR is derived and used as the design criterion. With maximum ratio combining, an iterative algorithm for obtaining suboptimal precoding matrices at the source and relay nodes is derived. Simulation shows that the algorithm takes very few iterations to give converged precoders for the source and relay nodes. The design algorithm can be applied to relay nodes with single-antenna for the benefit of less computational complexity and feedback overhead. Numerical results demonstrate that the proposed scheme provides a substantial performance gain over the existing strategies. A diversity order analysis is developed. Experimental results show that the theoretical analysis is quite close to simulation. The relay system using multiple-antenna at the relay nodes can considerably improve coding gain and/or diversity gain.