In-phase and quadrature-phase imbalance (IQI) at transceivers is one of the serious hardware impairments degrading system performance. In this paper, we study the overall performance of massive multi-user multi-input multi-output (MU-MIMO) systems with IQI at both the base station (BS) and user equipments (UEs), including the estimation of channel state information, required at the BS for the precoding design. We also adopt a widely-linear precoding based on the real-valued channel model to make better use of the image components of the received signal created by IQI. Of particular importance, we propose estimators of the real-valued channel and derive the closed-form expression of the achievable downlink rate. Both the analytical and simulation results show that IQI at the UEs limits the dowlink rate to finite ceilings even when an infinite number of BS antennas is available, and the results also prove that the widely-linear precoding based on the proposed channel estimation method can improve the overall performance of massive MU-MIMO systems with IQI.