In this paper, we propose a cross-layer design combining adaptive modulation coding (AMC) and automatic repeat request (ARQ) to minimize the bit energy consumption under both packet loss rate and retransmission delay constraints. We analyze the best constellation size of M-ary square quadrature amplitude modulation (MQAM) in different distance, and give advice on retransmission limits under different packet loss rates. The impacts of path loss fading and additive white Gaussian noise (AWGN)are taken into consideration. The computation of energy consumption includes the circuit, transmission and retransmission energies at both transmitter and receiver sides. Numerical results are obtained to verify the validity of our design. We also show that the retransmission benefit varies with the packet loss rate constraint.