Considering the issues of nonlinearity and self-interference in transmitting and receiving channels of a full-duplex MIMO radio respectively, a novel low hardware cost and low software complexity design scheme with transmitting channels linearization and self-interference cancellation by multi-tap RF cancellers and digital cancellers is proposed, where (1) An improved Cross-Talk Cancelling-Digital Pre-Distorter (CTC-DPD) algorithm and common feedback are used for decoupling and digital pre-distortion to make transmitting channels gain linearly and equally; (2) By introducing adjustable attenuators in receiving channels, multi-tap cancellers use received data along with minimum residual self-interference power criterion based multidimensional gradient descent method to search the multi-tap setting; (3) Digital self-interference is reconstructed for cancellation based on channel estimation in frequency domain. In the prototype of 20 MHz bandwidth LTE full-duplex 2×2 MIMO radio, transmitting channels have more flat in-band spectrum and 30 dB lower out-band noise after linearization. RF and digital self-interference cancellation need 0.17 ms for one turning and provide about 75 dB cancellation together. When two nodes with 16QAM mapping work at full-duplex mode, they achieve a sum of 220 Mbps bit rate, which double the bit rate of 110 Mbps at half-duplex mode and thus double the spectrum efficiency. The prototype demonstrates the feasibility of the proposed design.