Summary: We consider positive solutions of the Dirichlet problem for the fractional Laplace equation with singular nonlinearity \[ \begin{cases} (-\Delta)^s u(x) = K(x)u^{-\alpha}(x) + \mu u^{p-1}(x) &\text{in }\Omega,\\ u>0 &\text{in }\Omega,\\ u = 0 &\text{in }\Omega^c := \mathbb{R}^N\setminus\Omega, \end{cases} \] where \(s\in (0, 1)\), \(\alpha > 0\) and \(\Omega\subset\mathbb{R}^N\) is a bounded domain with smooth boundary \(\partial\Omega\) and \(N > 2s\). Under some appropriate assumptions of \(\alpha\), \(p\), \(\mu\) and \(K\), we obtain the existence of multiple weak solutions, and among them, including the minimal solution and a ground state solution. Radial symmetry of \(C^{1, 1}_{loc}\cap L^\infty\) solutions are also established for subcritical exponent \(p\) when the domain is a ball. Nonexistence of \(C^{1, 1}\cap L^\infty\) solutions are obtained for star-shaped domain under a condition of \(K\).