Motif discovery in DNA sequences is a challenging task in molecular biology. In computational motif discovery, Planted (l, d) motif finding is a widely studied problem and numerous algorithms are available to solve it. Both hardware and software accelerators have been introduced to accelerate the motif finding algorithms. However, the use of hardware accelerators such as FPGAs needs hardware specialists to design such systems. Software based acceleration methods on the other hand are easier to implement than hardware acceleration techniques. Grid computing is one such software based acceleration technique which has been used in acceleration of motif finding. However, drawbacks such as network communication delays and the need of fast interconnection between nodes in the grid can limit its usage and scalability. As using multicore CPUs to accelerate CPU intensive tasks are becoming increasingly popular and common nowadays, we can employ it to accelerate motif finding and it can be a faster method than grid based acceleration. In this paper, we have explored the use of multicore CPUs to accelerate motif finding. We have accelerated the Skip-Brute Force algorithm on multicore CPUs parallelizing it using the POSIX thread library. Our method yielded an average speed up of 34x on a 32-core processor compared to a speed up of 21x on a grid based implementation of 32 nodes.