Massive multiple-input multiple-output (MIMO) systems consist of a large number of antennas and radio frequency (RF) chains, which cause enormous circuit power consumption at the RF front ends. Since high-resolution analog-to-digital converters are the main contributor in the RF circuit power consumption, one-bit massive MIMO is considered as one of the potential solutions. The channel state information (CSI) acquisition in the presence of pilot contamination is a challenging task in such systems. In this paper, we present an iterative semi-blind-based channel estimation scheme for pilot contaminated one-bit multi-cell multi-user massive MIMO systems, which comprise of two stages: initialization and iteration. The initial channel estimate uses pilots in the initialization stage, which is further refined in the iteration stage with the help of both pilot and a few data symbols. We derive lower bounds on the uplink achievable rate with both perfect and imperfect CSI availability at the base station. Through simulations, we show that the proposed estimator achieves a considerable improvement in mean square error, bit-error-rate, power efficiency, and spectral efficiency from one-bit pilot-aided estimators at the cost of a nominal increase in computational complexity. Moreover, the proposed scheme in one-bit system achieves almost the same spectral efficiency as that of a pilot-aided estimator in an infinite-resolution-based massive MIMO system for lower values of signal-to-noise-ratio (SNR).