This paper considers an equalize-and-forward (EF) strategy for two-hop multiple-input multiple-output (MIMO) relay networks in multipath fading channels, where the relay nodes and the destination only know its respective backward channel state information (CSI) knowledge, and each node is equipped with multiple antennas for transmitting, receiving or forwarding signals. For such a relay network, the inter-symbol interference (ISI) and multiple-antenna interference (MAI) are two detrimental effect to degrade the bit error rate (BER) performance. In order to compensate for the interference problem, we design temporal-and-spatial (TS) equalizers to assist in forwarding and decoding the signals at the relay nodes and the destination node, respectively. Based on the minimum mean square error (MMSE) criterion with a total power constraint, an optimization framework is formulated to find the optimal TS equalizers with the backward CSI knowledge, and an iterative algorithm using the Karush-Kuhn-Tucker (K.K.T.) conditions is investigated to achieve the optimal solution. With these optimal TS equalizers, the MIMO relay network can not only effectively mitigate the interference but also provide both the spatial and multipath diversity gains. Simulation results indicate the effectiveness of the proposed algorithm, yielding a significant improvement on the BER performance.