Searching for an intermediate-range force has been considerable interests in gravity experiments. In this paper, aiming at a scalartensor 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 \documentclass[12pt]{minimal}
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$$\dot \omega$$
\end{document} of binary pulsars in harmonic coordinates is given. After that, \documentclass[12pt]{minimal}
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$$\dot \omega$$
\end{document} 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 α and λ. α and λ respectively represent the strength of the intermediate-range force coupling and its length scale. The limits from four binary pulsars data are respectively λ = (4.95±0.02)×108 m and α = (2.30±0.01)×10−8 if β = 1, where β is a parameter like standard parametrized post-Newtonian parameter βPPN. When three degrees of freedom (α, λ and β, \documentclass[12pt]{minimal}
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$$\bar \beta \equiv \beta - 1$$
\end{document}) in 1σ confidence level are considered, it yields α = (4.21 ± 0.01) × 10−4, λ = (4.51 ± 0.01) × 107 m and \documentclass[12pt]{minimal}
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$$\bar \beta = ( - 3.30 \pm 0.01) \times 10 - 3$$
\end{document}. Through our research on the scalar-tensor theory with the intermediate-range force, it shows that the parameter α is directly related to the parameter γ (α = (1 − γ)/(1 + γ)). Thus, this presents the constraints on 1 − γ by binary pulsars which is about 10−4 for three degrees of freedom.
