An alternating dependent variables (ADV) method is proposed to treat slip boundary conditions for interfacial flows of a nonspherical bubble in liquid when Cartesian velocity components are chosen as dependent variables in momentum equations written in nonorthogonal body-fitted coordinates. Cartesian interfacial velocities are solved alternatively at different segments of bubble profile, hence numerical instabilities due to a nearly infinite and zero slop of the profile are avoided. Numerical results indicate that the ADV is a suitable method for solving free surface flows of nonspherical bubbles with large curvature. On this basis, the interfacial characteristics of three types of nonspherical bubbles are presented.