We propose the improved GMSK (gaussian-filtered minimum shift keying) quadrature modulator using the FIR(finite impulse response )filter whose coefficients are obtained form the differnce of phase response, and design its ASIC (applicaton specific integrated circuit) which can be used for GSM (global system for mobile communication) digital cellular system and DCS 1800 (digital cellular system at 1800MHz) personal communication system. Input data become quantized I and Q channel 10 bit signal through cosine and sine ROM mapping after being filtered by the FIR filter whose normalized bandwidth is 0.3 and designed by considering intersymbol interference as well as sampling ratio. These two signals become the GMSK modulated I and Q channel signal through DAC (digital-to-analog converter) and 7th order analog chebyshev LPF(low pass filter) respectively. The difference between the ideal analog signal and its digitized signal is analyzed in terms of sampling noise, quantization noise, truncation noise and coefficient noise. And the effect of the LPF following the DAC is considered. The ASIC design of the GMSK quadrature modulator is also confirmed by an experiment.