Recently with the proliferating rates of digital data and the need of sending data through the internet, protection of the contents is crucial. This article proposes a quick method based on a combination of Linear Feedback Shift Register (LFSR) and Deoxyribonucleic acid (DNA) and Tinkerbell chaotic function. This method not only has high protection but also provides high encryption speed. First, a bit shift method is implemented in permutation phase. Shift numbers are determined by LSFR in each step. Then in each step of the permutation phase, specific numbers of pixels are delivered for final encryption in diffusion phase. In this phase, DNA as well as Tinkerbell index converts gray level of image pixels. The results show high security, incredible speed and good resistance against prevailing attacks.