Artificial synapse with good linearity is a critical issue in conductive bridging random access memory (CBRAM) synaptic device to accomplish an efficient learning approach in the artificial intelligence system. In this work, we investigate a novel approach to enhance the linearity of CBRAM synapse. The linearity of a memristive synapse can be improved by the high-temperature vacuum annealing process. The annealed device not only improves reliability such as endurance characteristics but also improves the synaptic characteristics including multilevel characteristics with varying RESET stop voltages from -0.60 to -1.40 V. The nonlinearities of potentiation and depression are 1.36 and -2.18 with 500 conductance pulses, respectively, and the device exhibits 720 training epochs with a total number of 720,000 pulse numbers. The post oxide annealed CBRAM device with analog switching behavior and excellent reliability is potential to be an artificial synapse for neuromorphic computing. In addition, the experimental potentiation and depression data are employed to train HNN for image processing of 30 x 30 pixels comprising 900 synapses. It is found that the HNN can be successfully trained to recognize the input image with a training accuracy of ~98% in 18 iterations.