In this paper, channel estimation for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems with one-bit analog-to-digital converters (ADCs) is considered. In the mmWave band, the number of propagation paths is small, which results in sparse virtual channels. To estimate sparse virtual channels based on the maximum a posteriori (MAP) criterion, sparsity-constrained optimization comes into play. In general, optimizing objective functions with sparsity constraints is NP-hard because of their combinatorial complexity. Furthermore, the coarse quantization of one-bit ADCs makes channel estimation a challenging task. In the field of compressed sensing (CS), the gradient support pursuit (GraSP) and gradient hard thresholding pursuit (GraHTP) algorithms were proposed to approximately solve sparsity-constrained optimization problems iteratively by pursuing the gradient of the objective function via hard thresholding. The accuracy guarantee of these algorithms, however, breaks down when the objective function is ill-conditioned, which frequently occurs in the mmWave band. To prevent the breakdown of gradient pursuit-based algorithms, the band maximum selecting (BMS) technique, which is a hard thresholder selecting only the band maxima, is applied to GraSP and GraHTP to propose the BMSGraSP and BMSGraHTP algorithms in this paper.