Truss-type structures are widely used in contemporary constructions. The dynamic analysis is very important to ensure the safety and the functionalities of these structures. The aim of this research was to propose a new method tailored for the dynamic analysis of linear truss-type structures. The proposed method is a single-step method underpinned by Unconventional Hamilton-type Variational Principles, and employing the finite element discretisation in both spatial and temporal domains. To develop the proposed method, five Unconventional Hamilton-type Variational Principles tailor-made for truss-type structures were derived, preserving naturally all necessary conditions for the dynamic analysis without the introduction of any artificial factors. The resultant one-field and the two-filed formulations were used to build algorithms for the proposed method. The semi-discretisation treatment of the spatial and temporal domains was applied to these formulations. While the spatial discretisation was undertaken in the standard fashion, temporal discretisation was attempted with four different types of time finite elements. The convergence of the algorithms was examined in terms of the stability and the consistency properties. Numerical examples with different types of truss-type structures were given to verify the proposed method, and also to compare the performance of these algorithms against the existing analysis methods. The proposed algorithms were shown to be second- or higher-order accurate when various time finite elements were employed. Compared to the widely used Average Acceleration Method (AAM), the proposed method produces highly accurate results. Larger time steps can be used without compromising the accuracy hence the computational costs may be reduced. Therefore, the proposed method can provide a fast and high-precision analysis solution for applications where these attributes are desired.