A compact on-chip dual-band bandpass filter (BPF) at millimeter-wave frequencies is proposed in 0.15-<inline-formula> <tex-math notation="LaTeX">${\mu }\text{m}$ </tex-math></inline-formula> GaAs technology. To understand the working mechanism of the BPF, an LC equivalent circuit model is presented and analyzed for position estimation of the transmission zeros and poles. For demonstration, an on-chip BPF example is fabricated and tested, whose simulation and measurement are in good agreement. There are two frequency bands at 60.2 and 79.7 GHz with bandwidths of 9% and 6.8%, respectively. The chip, excluding the feedings, is only 0.304 mm <inline-formula> <tex-math notation="LaTeX">$\times0.464$ </tex-math></inline-formula> mm.