As a follow-up on the drift-kinetic study of the non-local bootstrap current in the steep edge pedestal of tokamak plasma by Koh et al. [Phys. Plasmas 19 , 072505 (2012)], a gyrokinetic neoclassical study is performed with gyrokinetic ions and drift-kinetic electrons. Besides the gyrokinetic improvement of ion physics from the drift-kinetic treatment, a fully non-linear Fokker-Planck collision operator—that conserves mass, momentum, and energy—is used instead of Koh et al. 's linearized collision operator in consideration of the possibility that the ion distribution function is non-Maxwellian in the steep pedestal. An inaccuracy in Koh et al. 's result is found in the steep edge pedestal that originated from a small error in the collisional momentum conservation. The present study concludes that (1) the bootstrap current in the steep edge pedestal is generally smaller than what has been predicted from the small banana-width (local) approximation [e.g., Sauter et al. , Phys. Plasmas 6 , 2834 (1999) and Belli et al. , Plasma Phys. Controlled Fusion 50 , 095010 (2008)], (2) the plasma flow evaluated from the local approximation can significantly deviate from the non-local results, and (3) the bootstrap current in the edge pedestal, where the passing particle region is small, can be dominantly carried by the trapped particles in a broad trapped boundary layer. A new analytic formula based on numerous gyrokinetic simulations using various magnetic equilibria and plasma profiles with self-consistent Grad-Shafranov solutions is constructed.