We establish the pseudo-differential variant of the $L^{p}$ estimates for multi-linear and multi-parameter Coifman-Meyer multiplier operators proved by C. Muscalu, J. Pipher, T. Tao and C. Thiele in [?]. This gives an affirmative answer to the question, raised in the book of C. Muscalu and W. Schlag [?], on whether the $L^{p}$ estimates for multi-linear and multi-parameter pseudo-differential operators hold.