On-chip training of large-scale deep neural networks (DNNs) is challenging due to computational complexity and resource limitation. Compute-in-memory (CIM) architecture exploits the analog computation inside the memory array to speed up the vectormatrix multiplication (VMM) and alleviate the memory bottleneck. However, existing CIM prototype chips, in particular, SRAM-based accelerators target at implementing low-precision inference engine only. In this work, we propose a two-way SRAM array design that could perform bi-directional in-memory VMM with minimum hardware overhead. A novel solution of signed number multiplication is also proposed to handle the negative input in backpropagation. We taped-out and validated proposed two-way SRAM array design in TSMC 28nm process. Based on the silicon measurement data on CIM macro, we explore the hardware performance for the entire architecture for DNN on-chip training. The experimental data shows that proposed accelerator can achieve energy efficiency of ~3.2 TOPS/W, >1000 FPS and >300 FPS for ResNet and DenseNet training on ImageNet, respectively.