An efficient resistive random access memory (ReRAM) structure is developed for accelerating convolutional neural network (CNN) powered by the in-memory computation. A novel ReRAM cell circuit is designed with two-directional (2-D) accessibility. The entire memory system is organized as a 2-D array, in which specific memory cells can be identically accessed by both of column- and row-locality. For the in-memory computations of CNNs, only relevant cells in an identical sub-array are accessed by 2-D read-out operations, which is hardly implemented by conventional ReRAM cells. In this manner, the redundant access (column or row) of the conventional ReRAM structures is prevented to eliminated the unnecessary data movement when CNNs are processed in-memory. From the simulation results, the energy and bandwidth efficiency of the proposed memory structure are 1.4x and 5x of a state-of-the-art ReRAM architecture, respectively.