Summary: In this paper we prove the existence of at least one positive solution for nonlocal semipositone problem of the type \[ (P_{\lambda}^{\mu}) \begin{cases} (-\Delta)^s u & = \quad \lambda (u^q -1)+\mu u^r \text{ in } \Omega \\ \qquad u & > \quad 0 \text{ in } \Omega \\ \qquad u & \equiv \quad 0 \text{ on } \mathbb{R}^N \setminus\Omega. \end{cases} \] when the positive parameters \(\lambda\) and \(\mu\) belong to certain range. Here \(\Omega\subset \mathbb{R}^N\) is assumed to be a bounded open set with smooth boundary, \(s\in (0, 1), N> 2s\) and \(0<q<1<r\leq \frac{N+2s}{N- 2s}\). First we consider \((P_{\lambda}^{\mu})\) when \(\mu = 0\) and prove that there exists \(\lambda_0\in (0, \infty)\) such that for all \(\lambda > \lambda_0\) the problem \((P_{\lambda}^0)\) admits at least one positive solution. In fact we will show the existence of a continuous branch of maximal solutions of \((P_{\lambda}^0)\) emanating from infinity. Next for each \(\lambda >\lambda_0\) and for all \(0<\mu <\mu_{\lambda}\) we establish the existence of at least one positive solution of \((P_{\lambda}^{\mu})\) using variational method. Also in the sub critical case, i.e., for \(1<r<\frac{N+2s}{N-2s}\), we show the existence of second positive solution via mountain pass argument.