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The global stabilization of the Camassa-Holm equation with a distributed feedback control of the form −(λu−βuxx−λ[u])$-(\lambda u-\beta u_{xx}-\lambda[u])$ is investigated. The existence and uniqueness of global strong solutions and global weak solutions to the closed loop control system are obtained. The exponential asymptotical stabilization of weak solutions to the problem is established. Namely, the weak solutions to the problem exponentially uniformly decay to a constant. The main novelty in this paper is that the effects of the coefficients λ and β on the global existence and exponential asymptotical stabilization of solutions are given.