Existing constitutive laws of rock friction cannot describe both observed strengthening in the absence of slip and frictional behavior around steady-state sliding. Combining existing rate- and state-dependent friction laws, we propose a new friction law, which expresses logarithmically time-dependent healing at sliding velocities smaller than a cut-off velocity Vc and approaches the so-called slip law at velocities larger than Vc. Numerical simulations show that the new friction law adequately explains experimental results of velocity stepping tests and slide-hold-slide tests, which have widely been used to examine velocity-, time-, and displacement-dependent property of rock friction. Because the new friction law has a simple form and appears appropriate for a wide range of conditions, it is useful for application to numerical modeling of seismic cycles. ¿ 2001 American Geophysical Union