A new fractional two dimensional triangle function combination discrete chaotic map (2D-TFCDM) is proposed by utilizing the discrete fractional calculus. Furthermore, the chaos behaviors are numerically discussed in the fractional-order difference. The bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits are shown, respectively. With the keys produced by elliptic curve in finite field, the discrete fractional map is converted into algorithm, and applied to color image encryption. The image encryption method is first proposed by us worldwide. Keywords: Chaos, Discrete fractional calculus, Fractional 2D-TFCDM, Image encryption, Elliptic curve in finite field