The covariant phase space formalism of Iyer, Lee, Wald, Zoupas gives an elegant way to understand the Hamiltonian mechanics of gravity without breaking covariance. In this work, we revisit this formalism with more careful treatment of the boundary effect. We keep the boundary terms in the action from the very beginning, and derive the covariant phase space formalism systematically. Within our formalism, the Hamiltonian appears automatically only assuming that the configurations satisfy equations of motion and boundary conditions. We also give some comments on Peierls bracket which is a linear interpretation of bracket in covariant phase space formalism.

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