Bent functions have been applied to cryptography, spread spectrum, coding theory, and combinatorial design. Permutations play an important role in the design of cryptographic transformations such as block ciphers, hash functions and stream ciphers. By using the Kronecker product this paper presents a general recursive construction method of permutations over finite field. As applications of our method, several infinite classes of permutations are obtained. By means of the permutations obtained and M-M functions we construct several infinite families of bent functions.