Inhibitors targeting the amplification of the fibroblast growth factor receptor 1 (FGFR1) have found success in the treatment of FGFR1-positive squamous cell lung and breast cancers. A secondary mutation of gatekeeper residue (V561M) in the binding site has been linked to the acquired resistance. Recently, two well-known small molecule inhibitors of FGFR1, AZD4547 and E3810, reported that the V561M mutation confers significant resistance to E3810, while retaining affinity for AZD4547. FGFR1 is widely investigated as potential therapeutic target, while there are few computational studies made to understand the resistance mechanisms about FGFR1 V561M gatekeeper mutation. In this study, molecular docking, classical molecular dynamics simulations, molecular mechanics/generalized born surface area (MM/GBSA) free energy calculations, and umbrella sampling (US) simulations were carried out to make clear the principle of the binding preference of AZD4547 and E3810 toward FGFR1 V561M gatekeeper mutation. The results provided by MM/GBSA reveal that AZD4547 has similar binding affinity to both FGFR1 WT and FGFR1 V561M, whereas E3810 has much higher binding affinity to FGFR1 WT than to FGFR1 V561M. Comparison of individual energy terms indicates that the major variation of E3810 between FGFR1 WT and FGFR1 V561M are van der Waals interactions. In addition, US simulations prove that the potential of mean force (PMF) profile of AZD4547 toward FGFR1 WT and FGFR1 V561M has similar PMF depth. However, the PMF profile of E3810 toward FGFR1 WT and FGFR1 V561M has much higher PMF depth, suggesting that E3810 is more easily dissociated from FGFR1 V561M than from FGFR1 WT. The results not only show the drug-resistance determinants of FGFR1 gatekeeper mutation but also provide valuable implications and provide vital clues for the development of new inhibitors to combat drug resistance.