Due to the massive parallel computing capability and outstanding image and signal processing performance, cellular neural network (CNN) is one promising type of non-Boolean computing system that can outperform the traditional digital logic computation and mitigate the physical scaling limit of the conventional CMOS technology. The CNN was originally implemented by VLSI analog technologies with operational amplifiers and operational transconductance amplifiers as neurons and synapses, respectively, which are power and area consuming. In this paper, we propose a hybrid structure to implement the CNN with magnetic components and CMOS peripherals with a complete driving and sensing circuitry. In addition, we propose a digitally programmable magnetic synapse that can achieve both positive and negative values of the templates. After rigorous performance analyses and comparisons, optimal energy is achieved based on various design parameters, including the driving voltage and the CMOS driving size. At a comparable footprint area and operation speed, a spintronic CNN is projected to achieve about one order of magnitude energy reduction per operation compared to its CMOS counterpart.