  We explore the Minkowski functionals of weak lensing convergence map to
distinguish between $f(R)$ gravity and the general relativity (GR). The mock
weak lensing convergence maps are constructed with a set of high-resolution
simulations assuming different gravity models. It is shown that the lensing MFs
of $f(R)$ gravity can be considerably different from that of GR because of the
environmentally dependent enhancement of structure formation. We also
investigate the effect of lensing noise on our results, and find that it is
likely to distinguish F5, F6 and GR gravity models with a galaxy survey of
$\sim3000$ degree$^2$ and with a background source number density of
$n_g=30~{\rm arcmin}^{-2}$, comparable to an upcoming survey dark energy survey
(DES). We also find that the $f(R)$ signal can be partially degenerate with the
effect of changing cosmology, but combined use of other observations, such as
the cosmic microwave background (CMB) data, can help break this degeneracy.
