  We study the gradient flow equation for the O(N) nonlinear sigma model in two
dimensions at large N. We parameterize solution of the field at flow time t in
powers of bare fields by introducing the coefficient function X_n for the n-th
power term (n=1,3,...). Reducing the flow equation by keeping only the
contributions at leading order in large N, we obtain a set of equations for
X_n's, which can be solved iteratively starting from n=1. For n=1 case, we find
an explicit form of the exact solution. Using this solution, we show that the
two point function at finite flow time t is finite. As an application, we
obtain the non-perturbative running coupling defined from the energy density.
We also discuss the solution for n=3 case.
