In this paper, we study the use of adaptive modulation (AM) for a dual-hop multiple-input multiple-output (MIMO) network with transmit antenna selection (TAS) at the transmitter and maximal ratio combining (MRC) at the receiver. Our system deploys incremental amplify-and-forward (AF) relaying with AM to forward the source signal. A switching policy for selecting between the relaying and the direct communications is utilized to maximize spectrum efficiency. In particular, we derive expressions for the outage probability, spectrum efficiency, and bit error rate (BER) for the considered system over Nakagamim fading. The considered network not only takes advantage of TAS transmission such as achieving full diversity order with low transmit complexity but also inherits the beneficial feature of AM such as spectrum efficiency improvement.