To improve the classification accuracy of an image data set (CIFAR-10) by using analog input voltage, synapse devices with excellent conductance linearity (CL) and multi-level cell (MLC) characteristics are required. We analyze the CL and MLC characteristics of TaOx-based filamentary resistive random access memory (RRAM) to implement the synapse device in neural network hardware. Our findings show that the number of oxygen vacancies in the filament constriction region of the RRAM directly controls the CL and MLC characteristics. By adopting a Ta electrode (instead of Ti) and the hot-forming step, we could form a dense conductive filament. As a result, a wide range of conductance levels with CL is achieved and significantly improved image classification accuracy is confirmed.