  We propose a model for evolutionary game dynamics with three strategies $A$,
$B$ and $C$ in the framework of Moran process in finite populations. The model
can be described as a stochastic process which can be numerically computed from
a system of linear equations. Furthermore, to capture the feature of the
evolutionary process, we define two essential variables, the {\em global} and
the {\em local} fixation probability. If the {\em global} fixation probability
of strategy $A$ exceeds the neutral fixation probability, the selection favors
$A$ replacing $B$ or $C$ no matter what the initial ratio of $B$ to $C$ is.
Similarly, if the {\em local} fixation probability of $A$ exceeds the neutral
one, the selection favors $A$ replacing $B$ or $C$ only in some appropriate
initial ratios of $B$ to $C$. Besides, using our model, the famous game with
AllC, AllD and TFT is analyzed. Meanwhile, we find that a single individual TFT
could invade the entire population under proper conditions.
