  We study the potential of the galaxy cluster sample expected from the China
Space Station Telescope (CSST) survey to constrain dark energy properties. By
modelling the distribution of observed cluster mass for a given true mass to be
log-normal and adopting a selection threshold in the observed mass $M_{200m}
\geq 0.836 \times 10^{14} h^{-1}M_{\odot}$, we find about $4.1 \times 10^{5}$
clusters in the redshift range $0 \leq z \leq 1.5$ can be detected by the CSST.
We construct the Fisher matrix for the cluster number counts from CSST, and
forecast constraints on dark energy parameters for models with constant
($w_0$CDM) and time dependent ($w_0w_a$CDM) equation of state. In the
self-calibration scheme, the dark energy equation of state parameter $w_0$ of
$w_0$CDM model can be constrained to $\Delta w_0 = 0.036$. If $w_a$ is added as
a free parameter, we obtain $\Delta w_0 = 0.077$ and $\Delta w_a = 0.39$ for
the $w_0w_a$CDM model, with a Figure of Merit for ($w_0,w_a$) to be 68.99.
Should we had perfect knowledge of the observable-mass scaling relation
(``known SR" scheme), we would obtain $\Delta w_0 = 0.012$ for $w_0$CDM model,
$\Delta w_0 = 0.062$ and $\Delta w_a = 0.24$ for $w_0w_a$CDM model. The dark
energy Figure of Merit of ($w_0,w_a$) increases to 343.25. By extending the
maximum redshift of the clusters from $z_{max} \sim 1.5$ to $z_{max} \sim 2$,
the dark energy Figure of Merit for ($w_0,w_a$) increases to 89.72
(self-calibration scheme) and 610.97 (``known SR" scheme), improved by a factor
of $\sim 1.30$ and $\sim 1.78$, respectively. We find that the impact of
clusters' redshift uncertainty on the dark energy constraints is negligible as
long as the redshift error of clusters is smaller than 0.01, achievable by
CSST. We also find that the bias in logarithm mass must be calibrated to be
$0.30$ or better to avoid significant dark energy parameter bias.
