In this paper, we investigate the existence of infinitely many solutions for the following double phase problem $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} -\mathrm{div}(|\nabla u|^{p-2}\nabla u+a(x)|\nabla u|^{q-2}\nabla u)= f(x,u),&{}\hbox {in }\;\Omega , \\ u=0, &{}\hbox {on }\;\partial \Omega , \end{array} \right. \end{aligned}$$ - div ( | ∇ u | p - 2 ∇ u + a ( x ) | ∇ u | q - 2 ∇ u ) = f ( x , u ) , in Ω , u = 0 , on ∂ Ω , where $$N\ge 2$$ N ≥ 2 and $$1<p<q<N$$ 1 < p < q < N . Based on a direct sum decomposition of a space $$W_0^{1,H}(\Omega )$$ W 0 1 , H ( Ω ) , we prove that the above problem possesses multiple solutions under mild assumptions on a and f. The primitive of the nonlinearity f is of super-q growth near infinity in u and allowed to be sign-changing. Furthermore, our assumptions are suitable and different from those studied previously.