The arrayed waveguide grating (AWG) is an essential component in dense wavelength division multiplexing (DWDM) systems. With advancements in optical communication technology, the number of AWG output channels has rapidly increased. However, achieving high center frequency accuracy (CFA) for these channels has become a significant challenge. This paper presents a design and optimization approach for a high-channel-count AWG based on the silica platform and the finite difference beam propagation method (FD-BPM). The causes of center frequency deviation are analyzed, and an optimization method is proposed to adjust the constraint relationship and geometric position of the output waveguides in order to improve CFA. Simulation results demonstrate the excellent optical performance of the designed AWG, achieving a CFA of up to 0.04 times the output channel frequency spacing. The insertion loss, insertion loss uniformity, and adjacent output channel crosstalk are simulated as 1.51 dB, 0.38 dB, and 23.81 dB, respectively. The optimized CFA could compensate for center frequency deviations caused by manufacturing errors and temperature fluctuations. The findings of this research hold potential for extending the optimization to other material platforms and contributing to the development of DWDM systems in the field of optical communication.