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Voting is one of the important aspects of a democratic society in which people can express their opinions in a formal and legitimate way. In recent years, there has been an increasing interest in electronic voting (e-voting) systems. E-voting is a modern method of vote casting which is based on cryptographic tools. In many proposed scheme, it is a need to have a trusted entity to manage to take the votes and properly counting them. Recently and in the light of pivotal features of blockchain technology including immutability, transparency, and decentralization, blockchain based schemes have received considerable attention. In 2017, J. P. Cruz and Y. Kaji presented a blockchain based e-voting scheme with the help of some cryptographic concepts like bit-commitment and blind signatures. The vital property of their scheme was that it did not use any kind of anonymous channel which is a common and of course hard to implement tool in many e-voting protocols. In this paper, we address some security issues in the mentioned scheme and propose an improved version that has the edge on the prior one in terms of preserving privacy of voters and efficiency when it comes to large scale elections. We show how to use private blockchain instead of a public blockchain to provide more efficiency and privacy. Also, by utilizing proper entities, some security breaches like double voting are nrevented.