A FETI-DP (dual-primal finite element tearing and interconnecting) algorithm for the three-dimensional Stokes problem is developed and analyzed. This is an extension of the previous work for the two-dimensional problem in [H. H. Kim, C.-O. Lee, and E.-H. Park, SIAM J. Numer. Anal., 47 (2010), pp. 4142-4162]. Advantages of this approach are the coarse problem without primal pressure unknowns and the use of a computationally cheap lumped preconditioner. Especially in three dimensions, these advantages provide a more practical FETI-DP algorithm. In three dimensions, the velocity unknowns at subdomain corners and the averages of velocity unknowns over common faces are selected as the primal unknowns in the FETI-DP formulation. Its condition number bound is analyzed to be CH/h, where C is a positive constant which is independent of any mesh parameters and H/h is the number of elements across each subdomain. Numerical results are included.