The observability of charged Higgs bosons \(H^{\pm }\) has been investigated at future lepton collider in type I two-Higgs- doublet model (2HDM) at the center of mass energy \(\sqrt{s}=1.5\) TeV. The signal process chain is \( e^{+}e^{-} \rightarrow Z^{*}/ \gamma ^{*}\rightarrow H^{+} H^{-}\rightarrow H W^{+} H W^{-}\rightarrow b {\overline{b}} j j b {\overline{b}} j j\). The process proceeds through virtual \( \gamma \) and Z boson exchange in the s channel. Several benchmark points are selected, and events are analyzed to reconstruct the mass of charged Higgs bosons \( H^{\pm } \). The value of \(\tan \beta \) is kept relatively high to enhance the branching ratio of \( H\rightarrow b{\overline{b}} \) to benefit the signal processes. The main standard model (SM) background process produced is \( t{\overline{t}} \). Signal selection and significance efficiencies are calculated at integrated luminosities of 100 fb\(^{-1} \) , 500 fb\(^{-1}\), 1000 fb\(^{-1} \), and 5000 fb\(^{-1} \). The reconstructed and corrected mass of charged Higgs bosons \( H^{\pm } \) is determined. Analyzing the results demonstrates that charged Higgs bosons can be discovered through the pair production process via its bosonic decays. This study is supposed to provide the experimentalists with a good way to examine the Higgs bosons beyond SM and to check the validity of 2HDM models in considered parameter space.