In this talk we will present a fractional spectral method for a class of equations with non-smooth solutions.The proposed method makes new use of the classical fractional polynomials, also known as Muntz polynomials.We will show how to construct efficient fractional spectral methods for some integro-differential equations which can achieve spectral accuracy for solutions with limited regularity.A detailed convergence analysis will be provided.The potential application of this method covers a large number of problems, including classical elliptic equations,integro-differential equations with weakly singular kernels, fractional differential equations, and so on.