High frequency fishbone instability driven by passing energetic ions was first reported in the Princeton beta experiment with tangential neutral-beam-injection (Heidbrink et al 1986 Phys. Rev. Lett. 57835–8). It could play an important role for ITER-like burning plasmas, where α particles are mostly passing particles. In this work, a generalized energetic ion distribution function and finite drift orbit width effect are considered to improve the theoretical model for passing particle driving fishbone instability. For purely passing energetic ions with zero drift orbit width, the kinetic energy is derived analytically. The derived analytic expression is more accurate as compared to the result of previous work (Wang 2001 Phys. Rev. Lett. 865286–8). For a generalized energetic ion distribution function, the fishbone dispersion relation is derived and is solved numerically. Numerical results show that broad and off-axis beam density profiles can significantly increase the beam ion beta threshold for instability and decrease mode frequency.