A scalable deep-learning accelerator supporting the training process is implemented for device personalization of deep convolutional neural networks (CNNs). It consists of three processor cores operating with distinct energy-efficient dataflow for different types of computation in CNN training. Unlike the previous works where they implement design techniques to exploit the same characteristics from the inference, we analyze major issues that occurred from training in a resource-constrained system to resolve the bottlenecks. A masking scheme in the propagation core reduces a massive amount of intermediate activation data storage. It eliminates frequent off-chip memory accesses for holding the generated activation data until the backward path. A disparate dataflow architecture is implemented for the weight gradient computation to enhance PE utilization while maximally reuse the input data. Furthermore, the modified weight update system enables an 8-bit fixed-point computing datapath. The processor is implemented in 65-nm CMOS technology and occupies 10.24 mm(2) of the core area. It operates with the supply voltage from 0.63 to 1.0 V, and the computing engine runs in near-threshold voltage of 0.5 V. The chip consumes 40.7 mW at 50 MHz with the highest efficiency and achieves 47.4 mu J/epoch of training efficiency for the customized CNN model.