In this letter, uplink sum rate for multi-cell massive multi-user multiple-input multiple-output (MU-MIMO) systems with zero-forcing receivers is analyzed. To be practical, imperfect channel state information obtained through uplink training is assumed, and both large scale path loss and small scale fading effects are considered. A tight upper bound on sum rate is derived in closed form, which is applicable to MU-MIMO systems with any number of receiving antennas. The tightness of the upper bound is theoretically proved for massive MU-MIMO systems and is further demonstrated by computer simulations. The result thus enables a better understanding of multi-cell massive MU-MIMO systems and facilitates system design in practice.