By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), $t\ne t_j$, j ∈ ℤ, ⎨ ⎩$y\left(t{⁺}_j\right)=y\left(t{¯}_j\right)+I_j\left(y\left(t_j\right)\right)$, where $A\left(t\right)={\left(a_{ij}\left(t\right)\right)}_{n\times n}$ is a nonsingular matrix with continuous real-valued entries.