Dual-spectral computed tomography (DSCT) is used to reconstruct material- and energy-selective images to distinguish scanned object's materials and thus has numerous applications in medical and industrial fields. The image reconstruction method is vital in DSCT imaging, among which extended algebraic reconstruction technique (E-ART) can reconstruct basis material images with high quality. However, slow convergence limits its application. Herein, an accelerated extended algebraic reconstruction algorithm (AE-ART) was proposed. The main idea of the proposed algorithm is to increase the angle between the projection curves of high and low energies or to reduce the conditional number of coefficient matrix of those two projection curves by adding weights to the basis functions. Simulated experiments of dental phantom were conducted and the results indicated that the convergence rate of AE-ART was 30% higher than that of E-ART.