The　ball　screw　feed　system　(BSFS)　is　an　important　component　of　numerical　control　machine　tools.　The　dynamic　characteristics　of　BSFSs　directly　affect　the　machining　precision　and　efficiency　of　machine　tools.　Due　to　the　external　excitation,　the　feed　system　can　generate　large　vibrations,　which　can　further　decrease　the　precision　of　machine　tools.　This　paper　designs　multiple　tuned　mass　dampers　(MTMDs)　for　the　BSFS　to　reduce　the　vibration　and　proposes　a　dynamical　model　of　a　BSFS　with　MTMDs.　The　optimization　objective　is　to　minimize　the　maximum　amplitudes　of　the　lateral　direction　direct　frequency-response　function　of　the　work　table　at　different　nut　locations.　The　particle　swarm　optimization　algorithm　is　used　to　optimize　the　stiffness　and　damping　parameters　to　reach　the　optimal　vibration　reduction　effect.　Furthermore,　the　MTMDs　are　adjusted　quantitatively　to　match　the　optimized　dynamic　parameters　of　dampers.　By　comparing　the　experimental　modal　results　with　and　without　the　damper　and　the　vibration　signals　during　the　reciprocating　cycle　operation,　the　effect　of　the　damper　on　controlling　system　vibrations　is　verified.　The　results　indicate　that　the　proposed　lateral　vibration　control　method　for　the　BSFS　can　effectively　reduce　the　lateral　vibration　of　the　work　table　in　the　whole　stroke.