We study the following third-order p -Laplacian m -point boundary value problems on time scales ( ϕ p ( u Δ ∇ ) ) ∇ + a ( t ) f ( t , u ( t ) ) = 0 , t ∈ [ 0 , T ] T κ , u ( 0 ) = ∑ i = 1 m − 2 b i u ( ξ i ) , u Δ ( T ) = 0 , ϕ p ( u Δ ∇ ( 0 ) ) = ∑ i = 1 m − 2 c i ϕ p ( u Δ ∇ ( ξ i ) ) , where ϕ p ( s ) is p -Laplacian operator, that is, ϕ p ( s ) = | s | p − 2 s , p > 1 , ϕ p − 1 = ϕ q , 1 / p + 1 / q = 1 , 0 < ξ 1 < ⋯ < ξ m − 2 < ρ ( T ) . We obtain the existence of positive solutions by using fixed-point theorem in cones. In particular, the nonlinear term f ( t , u ) is allowed to change sign. The conclusions in this paper essentially extend and improve the known results.