As a novel non-volatile device, the memristive crossbar array has already delivered many of its promises including low computation complexity, high energy efficiency, and high density for the neuromorphic computing. However, the intrinsic variability of switching behavior has been a major obstacle to their implementation. Here we report a model that experimentally demonstrates the natural stochasticity of cycle-to-cycle variations and quantifies it. In addition, we propose level scaling and pulse regulating methods to mitigate the adverse impact of cycle-to-cycle variations. The relationship of the level of conductance and cycle-to-cycle variation is studied, and experiment results show an optimal number of the levels to mitigate cycle-to-cycle variations in the system. Additionally, the system compresses the number of pulses when the conductance is updated by the pulse stimulus to reduce cycle-to-cycle variations, resulting in the great energy and latency reduction. This work paves the way for the adoption of memristors for more efficient applications for the era of the edge computing and Internet of Things (IoT).