Time-domain chromatic dispersion (CD) equalization using finite impulse response (FIR) filter is now a common approach for coherent optical fiber communication systems. The complex weights of FIR filter taps are calculated from a truncated impulse response of the CD transfer function, and the modulus of the complex weights is constant. In our work, we take the limited bandwidth of a single channel signal into account and propose weighted FIR filters to improve the performance of CD equalization. A raised cosine FIR filter and a Gaussian FIR filter are investigated in our work. The optimization of raised cosine FIR filter and Gaussian FIR filter are made in terms of the EVM of QPSK, 16QAM and 32QAM coherent detection signal. The results demonstrate that the optimized parameters of the weighted filters are independent of the modulation format, symbol rate and the length of transmission fiber. With the optimized weighted FIR filters, the EVM of CD equalization signal is decreased significantly. The principle of weighted FIR filter can also be extended to other symmetric functions as weighted functions.