Chi et al. proposed a computationally efficient fast kurtosis maximization algorithm for blind equalization of multiple-input multiple-output linear time-invariant systems. This algorithm is also an iterative batch processing algorithm and has been applied to blind source separation. This paper considers blind beamforming of multiuser orthogonal frequency division multiplexing (OFDM) systems. Assuming that the channel is static within one OFDM block, a blind post-FFT multistage beamforming algorithm (MSBFA) based on subcarrier averaging is proposed. The algorithm basically comprises:( i) source (path signal) extraction using a hybrid beamforming algorithm composed of a Fourier beamformer and a kurtosis maximization beamformer, (ii) time delay estimation and compensation, (iii) classification (path-to-user association) and blind maximum ratio combining (of path signals). The designed beamformer is exactly the same for all the subcarriers, effectively utilizes multipath diversity for performance gain, and works well even in an environment with spatially correlated sources. Some simulation results are presented to demonstrate the effectiveness of the proposed MSBFA.