The rotation rate drift induced by optical Kerr effect in passive ring-resonator optical fiber gyroscope (PROG) using hollow-core photonic band-gap (HCPBG) fiber is different from that in the conventional single mode passive ring-resonator optical fiber gyroscope. To study the rotation rate drift induced by Kerr effect in the PROG system above, optical Kerr effect in the passive ring-resonator optical fiber gyroscope made from hollow-core photonic band-gap fiber is analyzed theoretically using a simple optical field overlap method, meanwhile, the numerical calculation is developed to study the system drift caused by Kerr effect. And it is compared with the Kerr effect of the passive ring-resonator optical fiber gyroscope made from conventional fiber. The theoretical evidence shows that optical Kerr effect induced by rotation rate shift in PROG made from hollow-core PBG fiber is reduced by 1～2 orders at different fiber loop lengths than that caused by ring-resonator optical fiber gyroscope made from conventional fiber when the spectral width optical source is fixed.