We propose a new on-chip optical neural network (OONN) based on multimode interfer-ence-microring resonators (MMI-RRs). The suggested structure eliminates the need for wave-length division multiplexers (WDM) to create an optical neuron on a single chip. New microring resonator structure based on 4x4 MMI coupler with a size of 24 & mu;m x 2900 & mu;m is used for the basic elements of the computation matrix, as a result a higher bandwidth and free spectral range (FSR) can be achieved. The Si3N4 platform along with the graphene sheet is designed to modu-late the signals and weights of the neural networks at a very high speed. The Si3N4 can provide wide range of operating wavelengths and can work directly with the wavelengths of color imag-es. The structure's benefits include rapid computing speed, little loss, and the ability to handle both positive and negative values. The OONN has been applied to the MNIST dataset with a speed faster than 2.8 to 14x times compared with the conventional GPU methods.