The head-on collision between two dust acoustic solitary waves in an unmagnetized strongly coupled dusty plasma with dust grains of negative charge and nonextensive ions and electrons are studied through the extended Poincaré-Lighthill-Kuo approach. Two Korteweg-de Vries equations are derived and accordingly two solitary wave solutions are obtained. In addition, an analytical expression for the phase shift due to the collision is derived. The nonextensivity effect of both ions and electrons on the characteristics of the head-on collision and the resulting phase shift due to the collision is studied. It is found that the characteristics of the head-on collision and the resulting phase shift strongly depend on the nonextensive parameter, the ratio of ion to electron densities as well as the ratio of ion to electron temperatures. The obtained results from this study can be used to understand the solitary waves interaction that may occur in plasma with dust impurities situations.