Cryptography is the art of keeping message secret by different methods. In this paper, a new algorithm has been proposed for symmetric key polyalphabetic data encryption, namely Fourier Masking Encryption Algorithm (FMEA). The concept of Fourier series is exploited efficiently to generate the random key sequence from a given password, as randomness is the key property of polyalphabetic encryption. It has been shown that the proposed algorithm can provide high level cryptanalytic complexity for any unauthorized attempt to decryption. Experimental results are also provided here, which shows the efficiency of the proposed one over the existing algorithms.