This paper proposes a new block cipher termed as "Modular Arithmetic based Block Cipher with Varying Key-Spaces (MABCVK)" that uses private key-spaces of varying lengths to encrypt data files. There is a simple but intelligent use of theory of modular arithmetic in the scheme of the cipher. Based on observed implementation of the proposed cipher on a set of real data files of several types, all results are tabulated and analyzed.The schematic strength of the cipher and the freedom of using a long key-space expectedly can make it reasonably nonvulnerable against possible cryptanalytic attacks. As a part of the future scope of the work, it is also intended to formulate and implement an enhanced scheme that will use a carrier image to have a secure transmission of the private key.