Interference alignment (IA) is a new approach to address interference in modern multiple-input multiple-out (MIMO) cellular networks in which interference is an important factor that limits the system throughput. System throughput in most IA implementation schemes is significantly improved only with perfect channel state information and in a high signal-to-noise ratio (SNR) region. Designing a simple IA scheme for the system with limited feedback and investigating system performance at a low-to-medium SNR region is important and practical. This paper proposed a precoding and user selection scheme based on partial interference alignment in two-cell downlink multiuser MIMO systems under limited feedback. This scheme aligned inter-cell interference to a predefined direction by designing user's receive antenna combining vectors. A modified singular value decomposition (SVD)-based beamforming method and a corresponding user-selection algorithm were proposed for the system with low rate limited feedback to improve sum rate performance. Simulation results show that the proposed scheme achieves a higher sum rate than traditional schemes without IA. The modified SVD-based beamforming scheme is also superior to the traditional zero-forcing beamforming scheme in low-rate limited feedback systems. The proposed partial IA scheme does not need to collaborate between transmitters and joint design between the transmitter and the users. The scheme can be implemented with low feedback overhead in current MIMO cellular networks.