A novel receiver optical system designed for Korean VLBI Network (KVN) has been used for conducting simultaneous millimeter-wave very long baseline interferometry (VLBI) observations at frequencies of 22, 43, 86, and 129 GHz. This multi-frequency band receiver system has been effective in compensation of atmospheric phase fluctuation by unique phase referencing technique in mm-VLBI observations. However, because the original optics system incorporated individual cryogenic receivers in separate cryostats, a rather bulky optical bench of size about 2600 mm x 2300 mm x 60 mm was required. To circumvent difficulties in installation and beam alignment, an integrated quasi-optical circuit incorporating a more compact triple-band receiver in single cryostat is proposed in this paper. The recommended frequency bands of the improved triple-band receiver are K(18-26 GHz) band, Q(35-50 GHz) band, and W(85-115 GHz) band. A frequency-independent quasi-optical circuit for triple band is adopted to obtain constant aperture efficiency as a function of the observed frequencies. The simulation results show that total aperture efficiency of each recommended frequency band is maintained almost constant within 1%. We present the design details of the compact wideband quasi-optical circuit and the triple-band receiver optimized for simultaneous multi-frequency observations.