Summary: We present some new embedding theorems on Campanato-Morrey spaces associated with vector fields satisfying Hörmander’s condition. The main theorem is \[ |f|_{{\mathcal L}^{p^*, \lambda}(\Omega)}\leq C\Biggl|\sum^m_{i= 1} |X_i, f|\Biggr|_{M^{p, \lambda}(\Omega)}, \] where \(X_1, \dots, X_m\) are \(C^\infty\) vector fields of Hörmander type. Unlike the Poincaré inequality, such embedding theorems allow larger gaps than \(1/Q\), which is known to be true for the Poincaré and Sobolev inequalities so far. As applications, we will study the local regularity of solutions to subelliptic PDE with coefficients in appropriate Campanato-Morrey spaces.