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In this work, we study the statistically robust beamforming design for an intelligent reflecting surfaces (IRS) assisted multiple-input single-output (MISO) wireless system under imperfect channel state information (CSI), where the channel estimation errors are assumed to be additive Gaussian. We aim at jointly optimizing the transmit/receive beamformers and IRS phase shifts to minimize the average mean squared error (MSE) at the user. In particular, to tackle the non-convex optimization problem, an efficient algorithm is developed by capitalizing on alternating optimization and majorization-minimization techniques. Simulation results show that the proposed scheme achieves robust MSE performance in the presence of CSI error, and substantially outperforms conventional non-robust methods.