This paper presents a new nonlinear feedback shift register (NLFSR) in the Galois configuration to generate the pseudorandom number sequences (PRNS) for a lightweight encryption scheme. In the NLFSR, the feedback function is applied to each state, not only the last bit of NLFSR. In the proposed design the size of the feedback is reduced using Galois configuration. The NLFSR is tested with NIST Statistical Test Suite to evaluate its quality randomness. The new NLFSR is used as an pseudorandom number generator to design a new lightweight image encryption algorithm. The encryption process can be represent in two phases permutation and diffusion. In the first phase, two different PRNSs generated by the new NLFSR for permute the row and column pixels of the plain image (PI). Then convert the permuted image into a 1D binary vector. In the diffusion phase, DNA arithmetic is applied between the 1D and another PRNS generated by the same NLFSR with different key. Several security analysis tests are performed on the proposed scheme (like histogram analysis, entropy, correlation coefficient, NPCR, UACI, MSE, and PSNR ) to test the security strength of the encryption method. It was found that the new NLFSR had passes all the tests in NIST Statistical Test Suite, and the test results of the encryption scheme are also acceptable and shows potential security strength.