This work investigates the progressive linear precoder design for packet retransmissions in multi-input multi-output (MIMO) systems with multiple codewords and automatic repeat request (ARQ) bundling feedback. Assuming perfect channel state information, a novel progressive linear ARQ precoder is proposed in the perspective of minimizing the packet error rate. We devise the ARQ precoder by combining power loading and subchannel pairing between current retransmission and previous transmissions. Furthermore, we extend the design to the case that the channel estimation error exists. Numerical results show that the proposed scheme can improve the performance of MIMO ARQ systems significantly regardless of the channel estimation error.