We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in(3 + 1)-dimensional spacetime;we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary(D + 1)dimensional spacetime;and we further find a recurrence relation among the spinor Feynman propagator in(D+1)-dimensional spacetime and the scalar Feynman propagators in(D+1)-,(D-1)-and(D+3)-dimensional spacetimes.