Summary: In this paper, we investigate the blow-up and global existence of solutions to the following time fractional nonlinear diffusion equations \[ \begin{aligned} ^C_0D^\alpha_t u-\Delta =|u|^{p-1},\quad & x\in\mathbb{R}^N,\;t> 0,\\ u(0,x)= u_0(x),\quad & x\in\mathbb{R}^N,\end{aligned} \] where \(0<\alpha<1\), \(p>1\), \(u_0\in C_0(\mathbb{R}^N)\) and \(^C_0D^\alpha_t u= (\partial/\partial t)_0I^{1-\alpha}(u(t,x)-u_0(x))\), \(_0I^{1-\alpha}_t\) denotes left Riemann-Liouville fractional integrals of order \(1-\alpha\). We prove that if \(1< p< 1+2/N\), then every nontrivial nonnegative solution blow-up in finite time, and if \(p\geq 1+ 2/N\) and \(\| u_0\|_{L^{q_c}(\mathbb{R}^N)}\), \(q_c= N(p-1)/2\) is sufficiently small, then the problem has global solution.