By numerically solving the three-dimensional time-dependent Schrödinger equation, we have invest-tigated multiphoton ionization of hydrogen atom in the two-color circularly polarized (TCCP) laser fields consisting of a strong 400 nm and a much weaker 800 nm pulses. Due to the presence of perturb-bative 800 nm laser pulse, sideband peaks emerge between the above-threshold ionization rings in the photoelectron momentum distributions. Our numerical results show that the sideband peaks exhibit one-lobe structure in the co-rotating TCCP laser fields, while it displays the three-lobe structure in the counter-rotating TCCP laser fields. Moreover, the photoelectron yield of sidebands in the co-rotating TCCP fields is much higher than those of the counter-rotating TCCP fields. These phenomena could be well explained from the perspective of the photon-absorption channels via the selection rules. In-terestingly, an obvious phase shift between the sidebands of different orders from the co-rotating and counter-rotating TCCP fields is observed. This shift indicates the helicity-dependent time delay in the one-photon continuum-continuum transition process.