  The varying speed of light (VSL) theory is controversial. It succeeds in
explaining some cosmological problems, but on the other hand it is excluded by
mainstream physics because it will shake the foundation of physics. In the
present paper, we devote ourselves to test whether the speed of light is
varying from the observational data of the type Ia Supernova, Baryon Acoustic
Oscillation, Observational $H(z)$ data and Cosmic Microwave Background (CMB).
We select the common form $c(t)=c_0a^n(t)$ with the contribution of dark energy
and matter, where $c_0$ is the current value of speed of light, $n$ is a
constant, and consequently construct a varying speed of light dark energy model
(VSLDE). The combined observational data show a much trivial constraint
$n=-0.0033 \pm 0.0045$ at 68.3\% confidence level, which indicates that the
speed of light may be a constant with high significance. By reconstructing the
time-variable $c(t)$, we find that the speed of light almost has no variation
for redshift $z < 10^{-1}$. For high-$z$ observations, they are more sensitive
to the VSLDE model, but the variation of speed of light is only in order of
$10^{-2}$. We also introduce the geometrical diagnostic $Om (z)$ to show the
difference between the VSLDE and $\Lambda$CDM model. The result shows that the
current data are difficult to differentiate them. All the results show that the
observational data favor the constant speed of light.
