In the hardware implementation of deep learning algorithms such as Convolutional Neural Networks (CNNs), vector-vector multiplications and memories for storing parameters take a significant portion of area and power consumption. In this paper, we propose a Domain Wall Memory (DWM) based design of CNN convolutional layer. In the proposed design, the resistive cell sensing mechanism is efficiently exploited to design a low-cost DWM-based cell arrays for storing parameters. The unique serial access mechanism and small footprint of DWM are also used to reduce the area and power cost of the input registers for aligning inputs. Contrary to the conventional implementation using Memristor-Based Crossbar (MBC), the bit-width of the proposed CNN convolutional layer is extendable for high resolution classifications and training. Simulation results using 65 nm CMOS process show that the proposed design archives 34% of energy savings compared to the conventional MBC based design approach.