Abstract The paper deals with the following double phase problem $$\begin{aligned} \begin{aligned}&-m \left[ \int _\Omega \left( \frac{|\nabla u|^p}{p} + a(x) \frac{|\nabla u|^q}{q}\right) \,\mathrm {d}x\right] {\text{div}} \left( |\nabla u|^{p-2}\nabla u + a(x) |\nabla u|^{q-2}\nabla u \right) \\&\quad = \lambda u^{-\gamma } +u^{p^*-1}&\quad \text {in } \Omega ,\\&u > 0&\quad \text {in } \Omega ,\\&u = 0&\quad \text {on } \partial \Omega , \end{aligned} \end{aligned}$$ -m∫Ω|∇u|pp+a(x)|∇u|qqdxdiv|∇u|p-2∇u+a(x)|∇u|q-2∇u=λu-γ+up∗-1inΩ,u>0inΩ,u=0on∂Ω, where $$\Omega \subset {\mathbb {R}}^N$$ Ω⊂RN is a bounded domain with Lipschitz boundary $$\partial \Omega $$ ∂Ω , $$N\ge 2$$ N≥2 , m represents a Kirchhoff coefficient, $$1<p<q<p^*$$ 1<p<q<p∗ with $$p^*=Np/(N-p)$$ p∗=Np/(N-p) being the critical Sobolev exponent to p , a bounded weight $$a(\cdot )\ge 0$$ a(·)≥0 , $$\lambda >0$$ λ>0 and $$\gamma \in (0,1)$$ γ∈(0,1) . By the Nehari manifold approach, we establish the existence of at least one weak solution.