This paper introduces a new type of free-form patches named rational boundary C2 Gregory patch. It can be said an extension of C2 Gregory patch developed by Miura and Wang, which gives users the capability of designing curvature-continuous surfaces (G2 continous surfaces) with reasonable flexibilities, and also that of rational boundary Gregory patch proposed by Chiyokura et al., which is surrounded by rational Bézier curves and can be interpolated with the continuity of tangent planes (G1 continuity). As the name of the patch implies, its boundary consists of rational Bézier curves. Its derivation is explained and methods for G2 continuity are proposed to connect it with a rational Bézier patch and with another RBC2G patch. Finally, a G2 continuous interpolation method based upon such patches is discussed.