A novel fractional two dimensional triangle function combination discrete chaotic maps (2DTFCDM) is proposed by taking use of the discrete fractional calculus. The chaos behaviors are then discussed in numerical aspect when the difference order is a fractional one. The bifurcation diagrams, the largest Lyapunov exponent plot and the phase portraits are displayed, respectively. Taking use of Elliptic curve in finite field as public key, we converted the discrete fractional maps into algorithm, and applied it in color image encryption of information security.