Employing low-resolution analog-to-digital converters (ADCs) coupled with large antenna arrays at the receivers has drawn considerable interests in the millimeter wave (mm-wave) system. Since mm-wave channels are sparse in angular dimensions, exploiting the structure could reduce the number of measurements while achieving acceptable performance at the same time. Motivated by the variational Bayesian line spectral estimation (VALSE) algorithm which treats the angles as random parameters, in contrast to previous works which confine the estimate to the set of grid angle points and induce grid mismatch, this paper proposes the grid-less quantized variational Bayesian channel estimation (GL-QVBCE) algorithm for antenna array systems with low resolution ADCs. Numerical results show the near optimal performance of GL-QVBCE by comparing with the Cramèr Rao bound (CRB) and the state-of-art methods.