In this paper, molecular dynamics (MD) simulations of the interaction between tilt grain boundaries (GBs) and a shuffle screw dislocation in silicon are performed. Results show that dislocations transmit into the neighboring grain for all GBs in silicon. For Σ3, Σ9 and Σ19 GBs, when a dislocation interacts with a heptagon site, it transmits the GB directly. In contrast, when interacting with a pentagon site, it first cross slips to a plane on the heptagon site and then transmits the GB. The energy barrier is also quantified using the climbing image nudged elastic band (CINEB) method. Results show that Σ3 GB provides a barrier for dislocation at the same level of the Peierls barrier. For both Σ9 and Σ19 GBs, the barrier from the heptagon sites is much larger than the pentagon sites. Since the energy barrier for crossing all the GBs at the heptagon sites is only slightly larger than the Peierls barrier, perfect screw dislocations cannot pile up against these GBs. Furthermore, the critical shear stress averaged over the whole sample for the transmission through the Σ9 and Σ19 GBs is almost twice on heptagon site for initially equilibrium dislocation comparing with dislocations moving at a constant velocity.