Constant modulus sequence having lower side-lobe levels in its auto-correlation function plays an important role in the applications like SONAR, RADAR and digital communication systems. In this paper, we consider the problem of minimizing the Integrated Sidelobe Level (ISL) metric, to design a complex unimodular sequence of any length. The underlying optimization problem is solved iteratively using the Block Majorization-Minimization(MM) technique, which ensures that the resultant algorithm to be monotonic. We also show a computationally efficient way to implement the algorithm using Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT) operations. Numerical experiments were conducted to compare the proposed algorithm with the state-of-the art algorithms and was found that the proposed algorithm performs better in terms of computational complexity and speed of convergence.