Election and voting play crucial roles in democratic society for an elactorate to make a collective decision. E-voting is one of the most challenging problems in cryptographic research to provide multiple dimensions security assurances. In this paper, we study an important voting paradigm, score voting, with privacy protection, which has not been investigated in previous work. We propose a blockchain based self-tallying election system to support score voting, dubbed “PriScore”, where the ballots are recorded on blockchain to prevent vote forgery or tampering. PriScore makes it possible for each voter to assign different evaluation scores (within a certain range) for the candidates as ranked-choice, where the sum of the scores in each ballot should be a predefined constant, and the evaluation scores are encrypted to maintain confidentiality. A major challenge in score voting is to simultaneously prove two constraint conditions: range proof and sum proof. We introduce a new technique, called dual zero-knowledge proof (dual-ZKP), to prove the scores satisfying two crucial requirements, which integrates “1-out-of- $K$ ” proof and distributed ElGamal crypto in a non-trivial way. The self-tallying mechanism in PriScore enables any party in the system to calculate and verify the election result, which provides fairness, dispute-freeness. The security analysis demonstrates that PriScore achieves completeness, soundness, eligibility, universal/individual verifiability and multiple-voting detection. We evaluate the performance of PriScore on modern workbench to test the performance, and also on a blockchain platform to measure the resource consumption. The experiments show that PriScore preserves privacy of score voting with reasonable overheads.