With the requirement for growth of massive connections in the fifth-generation (5G) system, there is an increasing challenge for traditional multiple access techniques to meet the needs of the exponentially increased number of terminals for the resource constrained networks. The sparse code multiple access (SCMA) technology has been proposed for the 5G communication systems to supply stronger connectivity with limited resources. However, a low-complexity decoding algorithm is required by the SCMA decoder for the high computation complexity of decoding nonorthogonal signals. In this paper, we propose a high-performance and low-cost decoding algorithm based on a Bayesian program learning method, Monte Carlo Markov Chain (MCMC). We also propose a new MCMC sampling method to generate samples from a joint update parallel (JUP) MCMC sampler. The simulation results show that the JUP-based MCMC SCMA decoder can save 60% computation complexity compared to the existing decoding method with a codebook size 16, which only has 0.5-dB performance loss compared to the maximum-likelihood-like decoding algorithm.