  First stars can only form in structures that are suitably dense, which can be
parametrized by the minimum dark matter halo mass $M_{\rm min}$. $M_{\rm min}$
must plays an important role in star formation. The connection of long
gamma-ray bursts (LGRBs) with the collapse of massive stars has provided a good
opportunity for probing star formation in dark matter halos. We place some
constraints on $M_{\rm min}$ using the latest $Swift$ LGRB data. We
conservatively consider that LGRB rate is proportional to the cosmic star
formation rate (CSFR) and an additional evolution parametrized as
$(1+z)^{\alpha}$, where the CSFR model as a function of $M_{\rm min}$. Using
the $\chi^{2}$ statistic, the contour constraints on the $M_{\rm
min}$--$\alpha$ plane show that at the $1\sigma$ confidence level, we have
$M_{\rm min}<10^{10.5}$ $\rm M_{\odot}$ from 118 LGRBs with redshift $z<4$ and
luminosity $L_{\rm iso}>1.8\times10^{51}$ erg $\rm s^{-1}$. We also find that
adding 12 high-\emph{z} $(4<z<5)$ LGRBs (consisting of 104 LGRBs with $z<5$ and
$L_{\rm iso}>3.1\times10^{51}$ erg $\rm s^{-1}$) could result in much tighter
constraints on $M_{\rm min}$, for which, $10^{7.7}\rm M_{\odot}<M_{\rm
min}<10^{11.6}\rm M_{\odot}$ ($1\sigma$). Through Monte Carlo simulations, we
estimate that future five years of Sino-French spacebased multiband
astronomical variable objects monitor (\emph{SVOM}) observations would tighten
these constraints to $10^{9.7}\rm M_{\odot}<M_{\rm min}<10^{11.3}\rm
M_{\odot}$. The strong constraints on $M_{\rm min}$ indicate that LGRBs are a
new promising tool for investigating star formation in dark matter halos.
