Recursive block Markov superposition transmission (rBMST) can be used to construct high-performance spatially coupled codes. When used in power-limited scenarios, low-complexity quantized decoders are required for the rBMST codes. In this letter, we introduce an efficient decoder for rBMST codes by incorporating non-uniform quantization (NUQ) into the threshold attenuated min-sum algorithm (TAMSA). The resulting decoder is referred to as the NUQ-TAMSA. We use the hierarchical dynamic quantization algorithm to design the non-uniform quantizer. To show the effectiveness of the NUQ-TAMSA, we carry out comprehensive comparisons. Our results show that, for low-resolution quantization, performance gains as large as 0.3 dB can be obtained with the NUQ-TAMSA. Numerical results also show that, for a wide range of coding rates, 5-bits non-uniform quantization is sufficient for NUQ-TAMSA to approach the performances of the floating-point based TAMSA.