We study a statistical ensemble of a single polymer with self gravitational interaction. This is a model of a gravitating string — the precursor of a black hole. We analyze averaged sizes by mean field approximations with an effective Hamiltonian a la Edwards with Newtonian potential as well as a contact repulsive interaction. We find that there exists a certain scaling region where the attractive and the repulsive forces balance out. The repulsive interaction pushes the critical gravitational coupling to a larger value, at which the size of a polymer becomes comparable to its Schwarzschild radius, and as a result the size of the corresponding black hole increases considerably. This talk is based on the joint work with T. Matsuo (NIT, Anan College), Prog. Theor. Exp. Phys. (2015) 123B02.