In this paper a modified transcendental equation is proposed, and we analyzed its chaotic characteristics and periodic. It is a simple non-linear mode, l but it has complex dynam ics.Then it was used in gray image encryption. This is a digital image encryption algorithm, dual scrambling that based on chaos of pixel position and pixel value.Compared with the traditional transcendental equation, the improved transcendental equation has only chaos characteristic, when the number of iterations is less than 5, the equation has periodicity,and when iterative times are more than 20, the equation has ...