Abstract
The object of the paper is to study a compact Lagrangian submanifold M in Kahler manifolds, such that the induced metric on the Lagrangian submanifolds is a conformal Ricci soliton with respect to potential vector field given by mean curvature vector field. Moreover, we also discuss the gradient conformal Ricci soliton and prove two characterizations of conformal Ricci soliton with the Laplace operator and the Poisson equation.