Nonlinear　parametric　vibration　of　an　axially　accelerating　viscoelastic　string　is　investigated.　The　string　is　constituted　by　the　fractional　Kelvin　model.　The　principal　parametric　resonance　is　analyzed　by　using　an　asymptotic　approach.　The　modulation　equation　is　derived　from　the　solvability　condition.　Closed-form　expressions　of　the　amplitudes　and　the　existence　conditions　of　steady-state　responses　are　obtained　from　the　modulation　equation.　Numerical　examples　are　presented　to　highlight　the　effects　of　fractional　order　and　other　system　parameters　on　the　responses.