Given positive integers k, $$\ell $$ ℓ and $$\lambda $$ λ such that $$2\leqslant \ell \leqslant k-1$$ 2⩽ℓ⩽k-1 , an $$(n,k,\ell ,\lambda )$$ (n,k,ℓ,λ) -hypergraph $$\mathcal {H}$$ H is a k-uniform hypergraph on the vertex set [n] in which every subset of size $$\ell $$ ℓ is contained in at most $$\lambda $$ λ edges. The independence number $$\alpha (\mathcal {H})$$ α(H) of $$\mathcal {H}$$ H is the maximum size of a subset of vertices which contains no edges of $$\mathcal {H}$$ H . Let $$f(n,k,\ell ,\lambda )=\min \{\alpha (\mathcal {H})\mid \mathcal {H}\ \mathrm{{is\ an\ }}(n,k,\ell ,\lambda )$$ f(n,k,ℓ,λ)=min{α(H)∣Hisan(n,k,ℓ,λ) -hypergraph$$\}$$ } . In this paper we show that for any given positive integers $$k\geqslant 5$$ k⩾5 , $$\frac{2k+4}{5}<\ell \leqslant k-2$$ 2k+45<ℓ⩽k-2 and $$\lambda \leqslant \left\lfloor \dfrac{n^{\frac{5\ell -2k-4}{3k-9}}}{\omega (n)}\right\rfloor $$ λ⩽n5ℓ-2k-43k-9ω(n) , $$\begin{aligned} f(n,k,\ell ,\lambda )\geqslant C_{k,\ell }\left( \frac{n}{\lambda }\log \frac{n}{\lambda }\right) ^{\frac{1}{\ell }}, \end{aligned}$$ f(n,k,ℓ,λ)⩾Ck,ℓnλlognλ1ℓ, where $$\omega (n)\rightarrow \infty $$ ω(n)→∞ arbitrarily slowly as $$n\rightarrow \infty $$ n→∞ and $$C_{k,\ell }$$ Ck,ℓ is a constant depending only on k and $$\ell $$ ℓ . In particular, $$C_{k,\ell }\sim \frac{\ell -1}{e}$$ Ck,ℓ∼ℓ-1e as $$k\rightarrow \infty $$ k→∞ . It generalizes the results from the case $$\ell =k-1$$ ℓ=k-1 or $$\lambda =1$$ λ=1 . An upper bound on $$f(n,k,\ell ,\lambda )$$ f(n,k,ℓ,λ) is also obtained for $$k\geqslant 3$$ k⩾3 , $$2\leqslant \ell \leqslant k-1$$ 2⩽ℓ⩽k-1 and $$\log n\ll \lambda \ll n$$ logn≪λ≪n , by considering a random k-uniform hypergraph $$\mathcal {H}_k(n,p)$$ Hk(n,p) .