The potential performance gains promised by massive multi-input and multioutput (MIMO) rely heavily on the access to accurate channel state information (CSI), which is difficult to obtain in practice when channel coherence time is short and the number of mobile users is huge. To make the system with imperfect CSI perform well, we propose a rateless codes-aided massive MIMO scheme, with the aim of approaching the maximum achievable rate (MAR) as well as improving the achieved rate over that based on the fixed-rate codes. More explicitly, a recently proposed family of rateless codes, called spinal codes, are applied to massive MIMO systems, where the spinal codes bring the benefit of approximately achieving the MAR with sufficiently large encoding block size. In addition, the multilevel puncturing and dynamic block-size allocation (MPDBA) scheme is proposed, where the block sizes are determined by user MAR to curb the average retransmission delay for successfully decoding the messages, which further enhances the system retransmission efficiency. Multilevel puncturing, which is MAR dependent, narrows the gap between the system MAR and the related achieved rate. Theoretical analysis is provided to demonstrate that spinal codes with the MPDBA can guarantee the system retransmission efficiency as well as achieved rate, which are also verified by numerical simulations. Finally, a simplified but comparable MIMO testbed with 2 transmit antennas and 2 single-antenna users, based on NI Universal Software Radio Peripheral (USRP) and LabVIEW communication toolkits, is built up to demonstrate the effectiveness of our proposal in realistic wireless channels, which is easy to be extended to massive MIMO scenarios in future.