This paper presents the structural design and optimization of a novel structure-based bistable vibration energy harvester with more adjustability, which can be well applied in various situations. Its unique feature is that the stiffness system is composed of a precompressed beam and a positive-stiffness beam. Its bistability can be adjusted by changing the structural parameters of the precompressed beam and positive-stiffness beam. Thus, the proposed harvester enables more adjustability than a common structure-based bistable vibration energy harvester. In addition, when the input excitation has the effect of gravity, the gravity effect can be wiped out by preloading a displacement to the fixed end of the positive-stiffness beam. To identify the structural parameters which affect the performance of the proposed harvester, an analytical model is established. Based on the finite element analysis, a design optimization is conducted to find out the optimal structural parameters under the constraints. The mechanism performance is verified by performing simulation study based on finite element analysis.