By using a multiple fixed point theorem (Avery-Peterson fixed point theorem) for cones, some criteria are established for the existence of three positive periodic solutions for a class of higher-dimensional functional differential equations with impulses on time scales of the following form: x Δ ( t ) = A ( t ) x ( t ) + f ( t , x t ) , t ≠ t j , t ∈ 𝕋 , x ( t j + ) = x ( t j − ) + I j ( x ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × n is a nonsingular matrix with continuous real-valued functions as its elements. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.