Multibeam massive multiple-input multiple-output (MIMO) configuration has been proposed that selects high-power beams in an analog part and uses a blind algorithm, such as the constant-modulus algorithm (CMA), in the digital part. The CMA does not require channel state information. However, when least-squares CMA (LS-CMA) is applied to a quadrature amplitude modulation signal whose amplitude changes, the interference cancellation effect decreases as the modulation order increases. In this paper, a variable-step-size-based CMA (VS-CMA), which modifies the step size of the steepest-descent CMA, is proposed as a blind adaptive algorithm to replace LS-CMA. The basic performance of VS-CMA, its success in cancelling interference, and its effectiveness in multibeam massive MIMO transmission are verified via simulation and compared with other blind algorithms such as independent component analysis, particularly when the data smoothing size is small.