Compared to the linear MIMO detectors, the Belief Propagation (BP) detector has shown greater capabilities in achieving near-optimal performance and better nature to iteratively cooperate with channel decoders. Aiming at real applications, recent works mainly fall into the category of reducing the complexity by simplified calculations, at the expense of performance sacrifice. However, the complexity is still unsatisfactory with exponentially increasing complexity or required exponentiation operations. Furthermore, the state-of-the-art (SOA) BP detectors persistently encounter error floor in high signal-to-noise ratio (SNR) region, which becomes even worse with calculation approximation. This work aims at a revised BP detector, named Belief-selective Propagation (BsP) detector by selectively utilizing the trusted incoming messages with sufficiently large a priori probabilities for updates. Two proposed strategies: symbol-based truncation (ST) and edge-based simplification (ES) squeeze the complexity (orders lower than the BP detector), while greatly relieving the error floor issue over a wide range of antenna and modulation combinations. For the 256-QAM 128 chi 64 uplink massive multiuser MIMO (MU-MIMO) system, the B(1,1) BsP detector achieves more than 1dB performance gain (@BER=10(-4)) with lower complexity than the state-of-the-art (SOA) BP detector. Trade-off between performance and complexity towards different application requirements can be conveniently obtained by tuning the parameters of the ST and ES strategies.