  This paper proposes a global Pad\'{e} approximation of the generalized
Mittag-Leffler function $E_{\alpha,\beta}(-x)$ with $x\in[0,+\infty)$. This
uniform approximation can account for both the Taylor series for small
arguments and asymptotic series for large arguments. Based on the complete
monotonicity of the function $E_{\alpha,\beta}(-x)$, we work out the global
Pad\'{e} approximation [1/2] for the particular cases $\{0<\alpha<1,
\beta>\alpha\}$, $\{0<\alpha=\beta<1\}$, and $\{\alpha=1, \beta>1\}$,
respectively. Moreover, these approximations are inverted to yield a global
Pad\'{e} approximation of the inverse generalized Mittag-Leffler function
$-L_{\alpha,\beta}(x)$ with $x\in(0,1/\Gamma(\beta)]$. We also provide several
examples with selected values $\alpha$ and $\beta$ to compute the relative
error from the approximations. Finally, we point out the possible applications
using our established approximations in the ordinary and partial
time-fractional differential equations in the sense of Riemann-Liouville.
