The Aztec diamond was extensively studied in both graph theory and statistical physics. Knuth obtained a formula of the number of spanning trees of the Aztec diamond with the constrained boundary condition, which solved a conjecture posed by Stanley in 1994. In this paper. We give the formulae of the energy and the number of spanning trees of the Aztec diamond with the toroidal boundary condition. (C) 2010 Elsevier B.V. All rights reserved