Link adaptation techniques have recently been proposed as a spectrally efficient method of obtaining high quality service for mobile communication systems. These schemes aim to better utilise channel capacity compared to fixed transmission schemes, by adapting signal transmission parameters, such as modulation constellation and transmit power. Adaptive modulation schemes, which adapt the modulation constellation, have gained considerable favour for exploiting time-varying channel conditions without increasing the level of co-channel interference. However, the traditional adaptive modulation schemes are designed assuming zero delay between the channel estimation and the modulation mode adaptation. In the case of non-zero delay, the transmitter would update the modulation mode based on outdated channel state information from the receiver. In this paper, we investigate an adaptive quadrature amplitude modulation (AQAM) scheme, which by way of retransmissions, allows a targeted reliability level to be met even in the presence of non-zero delay. The effect of non-zero delay on performance is then investigated. Closed form expressions for the average number of bits per symbol (BPS) throughput and the average bit error rate (BER) of the proposed scheme are derived.