We study general rotating string solution in the AdS(4) X CP**3 background with a B_NS holonomy turned on over ${bf CP}^1$ $subset $ $ {bf CP}^3$. We find the giant magnon and single spike solutions for the string moving in this background correspond
ing to open spin chain. We calculate the corresponding dispersion relation among various conserved charges for both the cases. We further study the finite size effect on both the giant magnon and single spike solutions.
