<p>We present a quantum inference algorithm for discrete Bayesian networks using quantum rejection sampling and a quantum circuit construction method to deal with conditional probabilities for discrete random variables having more than two probability events. To eliminate the iterative process of the quantum rejection sampling, a fixed-point quantum search method is used in the inference algorithm, which achieves a square-root speedup over its classical counterparts. The implementation of conditional probabilities uses ancilla registers, Hadamard gates, and multi-controlled rotation-Y gates. Experiments involving three Bayesian networks taken from the literature and one based on responses to a Web survey show the validity of the proposed methods. The inferred probability distributions produced in the experiments are nearly identical to those produced by a classical inference algorithm, implying that the proposed methods are applicable to Bayesian networks representing real-life applications.</p>