An improved transcendental equation and new image encryption algorithm is proposed. Compared with the logistic mapping and the transcendental equation, the modified chaotic equation has larger key space, and the generated chaotic sequences has excellent performance such as cross correlation and sensitivity. The modified transcendental equation was used in biological image encryption, and the encryped image was embedded in a carrier image using the LSB(least significant bit) algorithm. Theoretical analyses and experimental results show that the equation and the algorithm has more efficiency and security, it can resist violence attack, known-plaintext attack and statistical analysis effectively