In this paper, we consider filter-and-forward relay beamforming using orthogonal frequency-division multiplexing (OFDM) in the presence of inter-block interference (IBI). We propose a filter design method based on a constrained max-min problem, which aims to suppress IBI and also avoid deep nulls in the frequency domain. It is shown that IBI can be suppressed completely owing to the employment of beamforming with multiple relays or multiple receive antennas at each relay when perfect channel state information (CSI) is available. In addition, we modify the proposed method to cover the case where only the partial CSI for relay-receiver channels is available. Numerical simulation results show that the proposed method significantly improves the performance as the number of relays and antennas increases due to spatial diversity, and the modified method can make use of the channel correlation to improve the performance.