  In this paper, we study the convergence of the nonsymmetric interior penalty
Galerkin (NIPG) method on a Bakhvalov-type mesh for the first time. For this
purpose, a new composite interpolation is designed, which solves the inherent
difficulty of analysis on Bakhvalov-type meshes. More specifically, Gauss Radau
interpolation and Gauss Lobatto interpolation are used outside and inside the
layer, respectively. On the basis of that, by choosing the specific values of
the penalty parameters at different mesh points, we derive the supercloseness
of $k+1/2$th order ($k\ge 1$), and prove the convergence of optimal order in an
energy norm. The theoretical conclusion is consistent with the numerical
results.
