A {\it regular balanced Cayley map} (RBCM for short) on a finite group $Γ$ is an embedding of a Cayley graph on $Γ$ into a surface, with some special symmetric property. People have classified RBCM's for cyclic, dihedral, generalized quaternion, dicyclic, and semi-dihedral groups. In this paper we classify RBCM's on the group ${\rm PSL}(2,p)$ for each prime number $p>3$.