This paper deals with the quasilinear degenerate chemotaxis system with flux limitation $$\begin{aligned} \textstyle\begin{cases} u_{t} = \nabla \cdot \biggl(\frac{u^{p} \nabla u}{\sqrt{u^{2} + | \nabla u|^{2}}} \biggr) -\chi \nabla \cdot \biggl( \frac{u^{q} \nabla v}{\sqrt{1 + |\nabla v|^{2}}} \biggr), &x\in \varOmega ,\ t>0, \\ 0 = \Delta v - \mu + u, &x\in \varOmega ,\ t>0, \end{cases}\displaystyle \end{aligned}$$ where \(\varOmega := B_{R}(0) \subset \mathbb{R}^{n}\) (\(n \in \mathbb{N}\)) is a ball with some \(R>0\), and \(\chi >0\), \(p,q\geq 1\), \(\mu := \frac{1}{| \varOmega |} \int _{\varOmega }u_{0}\) and \(u_{0}\) is an initial data of an unknown function \(u\). Bellomo–Winkler (Trans. Am. Math. Soc. Ser. B 4, 31–67, 2017) established existence of an initial data such that the corresponding solution blows up in finite time when \(p=q=1\). This paper gives existence of blow-up solutions under some condition for \(\chi \) and \(u_{0}\) when \(1\leq p\leq q\).