The traditional degree distributions for the design of rateless codes do not perform well in latency and decoding success rate for short codes, and their encoding and decoding complexity is relatively high. This letter proposes an optimized degree distribution with lower encoding and decoding complexity. It keeps the average degree constant at a smaller value with the increasing of the source symbol length $k$ , making the encoding and decoding complexity reduced and no longer grow exponentially with $k$ . By increasing the mean of the ripple size, reducing its variance, and limiting the number of repeated degree-1 encoded symbols in the ripple, a convex optimization model is established and solved by Sequential Quadratic Programming. Simulation results show that compared with other degree distributions, the optimized degree distribution performs better in latency and decoding success rate for short codes and has lower encoding and decoding complexity.