We study the robust linear equalizer for the uplink of massive multiple-input-multiple-output (MIMO) systems with multi-cell pilot reuse. We use the worstcase approach for robust design in order to combat pilot contamination. When the number of the base station (BS) antennas is large, we build a novel model to indicate the relationship between the instantaneous channel matrix and the imperfect channel estimation in the presence of channel model uncertainty. Based on this model, we formulate the robust equalizer design problem into a minmax problem. Further, we transform the min-max problem to an unconstrained one, and the optimality conditions are derived. With the resulting optimality conditions, two iterative algorithms and a simple approximation method are proposed to compute the optimal robust equalizers. Simulations are adopted to evaluate the performance of the proposed algorithms and approximation method. Compared to the conventional equalizers, the proposed robust equalizers achieve better bit-error-rate (BER) performance, especially in the regime of high signal-to-noise ratio (SNR), where pilot contamination is significant.