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Model counting is the number of models for a given proposition formula, which is a basic problem in the field of artificial intelligence. There are many exactly-one constraints in many practical problems such as Bayesian networks, bounded model detection, and accurate set coverage. A common processing method is to encode exactly-one constraints as CNF formulas, and then call the model counter to solve them. This method expands the scale of the proposition formula and easily leads to too long solution time. This paper respectively proposes the ECR algorithm that restores exactly-one constraints from the CNF formula and the ECP algorithm that handles exactlyone constraints. The ECR algorithm can significantly improve the solution efficiency of the C2D compiler. Based on the latest model counter ExactMC, this paper improves the model counter ECMC that can recognize and handle exactly-one constraints separately. The experimental results show that the time efficiency of ECMC is significantly improved compared to ExactMC. [ABSTRACT FROM AUTHOR]