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The main objective of this article is to present an efficient numerical method to solve the delay differential equation of fractional order. We use the Caputo's fractional derivative for solving the fractional differentiation. The properties of shifted Chebyshev polynomials are exploited to reduce the Delay Fractional Differential Equation (DFDE) to a linear or non-linear easily solvable system of algebraic equations. A comparison is given between the present method and Adomian Decomposition Method (ADM) with the help of solved numerical illustrative example. The results shows that proposed method is very effective and simple. Which reveals the validity and applicability of the method. [ABSTRACT FROM AUTHOR]