A reduced complexity multiple-input multiple-output (MIMO) channel estimator known as the polynomial-predictor-based vector generalized least mean squares (VGLMS) estimator is developed. It is a simplification of a previously developed polynomial-predictor-based vector generalized recursive least squares (VGRLS) estimator, achieved by replacing the online recursive computation of the 'intermediate' matrix by an offline pre-computed matrix. Similar to the VGRLS estimator, it is able to operate in Rayleigh or Rician fading environments without reconfiguration of the state transition matrix to accommodate the non-random mean components. It is seen to offer a trade-off between reduced complexity channel estimation and good system performance.