This paper describes an implementation of spatial consistency in the NYUSIM channel simulation platform. NYUSIM is a millimeter wave (mmWave) channel simulator that realizes measurement-based channel models based on a wide range of multipath channel parameters, including realistic multipath time delays and multipath components that arrive at different 3-D angles in space, and generates life-like samples of channel impulse responses (CIRs) that statistically match those measured in the real world. To properly simulate channel impairments and variations for adaptive antenna algorithms or channel state feedback, channel models should implement spatial consistency which ensures correlated channel responses over short time and distance epochs. The ability to incorporate spatial consistency into channel simulators will be essential to explore the ability to train and deploy massive multiple-input and multiple-output (MIMO) and multi-user beamforming in next-generation mobile communication systems. This paper reviews existing modeling approaches to spatial consistency, and describes an implementation of spatial consistency in NYUSIM for when a user is moving in a square area having a side length of 15 m. The spatial consistency extension will enable NYUSIM to generate realistic evolutions of temporal and spatial characteristics of the wideband CIRs for mobile users in motion, or for multiple users who are relatively close to one another.