  Searching for an intermediate-range force has been considerable interests in
gravity experiments. In this paper, aiming at a scalar-tensor theory with an
intermediate-range force, we have derived the metric and equations of motion
(EOMs) in the first post-Newtonian (1PN) approximation for general matter
without specific equation of state and $N$ point masses firstly. Subsequently,
the secular periastron precession $\dot{\omega}$ of binary pulsars in harmonic
coordinates is given. After that, $\dot{\omega}$ of four binary pulsars data
(PSR B1913+16, PSR B1534+12, PSR J0737-3039 and PSR B2127+11C) have been used
to constrain the intermediate-range force, namely, the parameters $\alpha$ and
$\lambda$. $\alpha$ and $\lambda$ respectively represent the strength of the
intermediate-range force coupling and its length scale. The limits from four
binary pulsars data are respectively $\lambda=(4.95\pm0.02)\times10^{8}$m and
$\alpha=(2.30\pm0.01)\times10^{-8}$ if $\beta=1$ where $\beta$ is a parameter
like standard parametrized post-Newtonian parameter $\beta_{PPN}$. When three
degrees of freedom ($\alpha$, $\lambda$ and $\bar{\beta}\equiv\beta-1$) in
1$\sigma$ confidence level are considered, it yields
$\alpha=(4.21\pm0.01)\times10^{-4}$, $\lambda=(4.51\pm0.01)\times10^{7}$m and
$\bar{\beta}=(-3.30\pm0.01)\times10^{-3}$. Through our research on the
scalar-tensor theory with the intermediate-range force, it shows that the
parameter $\alpha$ is directly related to the parameter $\gamma$
($\alpha=(1-\gamma)/(1+\gamma)$). Thus, this presents the constraints on
$1-\gamma$ by binary pulsars which is about $10^{-4}$ for three degrees of
freedom.
