Three-dimensional vertical resistive random access memory (VRRAM) is proposed as a promising candidate for increasing resistive memory storage density, but the performance evaluation mechanism of 3-D VRRAM arrays is still not mature enough. The previous approach to evaluating the performance of 3-D VRRAM was based on the write and read margin. However, the leakage current (LC) of the 3-D VRRAM array is a concern as well. Excess leakage currents not only reduce the read/write tolerance and liability of the memory cell but also increase the power consumption of the entire array. In this article, a 3-D circuit HSPICE simulation is used to analyze the impact of the array size and operation voltage on the leakage current in the 3-D VRRAM architecture. The simulation results show that rapidly increasing leakage currents significantly affect the size of 3-D layers. A high read voltage is profitable for enhancing the read margin. However, the leakage current also increases. Alleviating this conflict requires a trade-off when setting the input voltage. A method to improve the array read/write efficiency is proposed by analyzing the influence of the multi-bit operations on the overall leakage current. Finally, this paper explores different methods to reduce the leakage current in the 3-D VRRAM array. The leakage current model proposed in this paper provides an efficient performance prediction solution for the initial design of 3-D VRRAM arrays.