To predict the coning motion forms of a rolling projectile with configurational asymmetries, the nonlinear characteristics for the system are investigated in this paper. The nonlinear dynamic model of rolling projectiles in coning motion is built by considering the nonlinear aerodynamics and roll orientation-dependent aerodynamics. The configurational asymmetry is modeled as a periodically parametric excitation in order to study its effect on the periodic response stability of the rolling projectile. Numerical continuation method is resorted to determine the parametric zone for the steady motions, and the possible stable rotational speeds are discussed. The numerical simulations, Lyapunov exponent spectrum analysis and Poincare sections are performed to confirm the existence of chaotic coning motion. The results shown in this study not only contribute to an in-depth understanding for the nonlinear dynamics of rolling projectiles but also provide an important reference for the further study of the control design for the yaw-pitch-roll coupling of asymmetric rolling projectiles with nonlinear aerodynamics.