A single electro-optical (EO) sensor used in space debris observation provides angle-only information. However, space debris position can be derived using simultaneous optical measurements obtained from two EO sensors located at two separate observation sites, and this is commonly known as triangulation. In this paper, we propose a new triangulation algorithm to determine space debris position, and its analytical expression of Root-Mean-Square (RMS) position error is presented. The simulation of two-site observation is conducted to compare the RMS positioning error of the proposed triangulation algorithm with traditional triangulation algorithms. The results show that the maximum RMS position error of the proposed triangulation algorithm is not more than 200 m, the proposed triangulation algorithm has higher positioning accuracy than traditional triangulation algorithms, and the RMS position error obtained in the simulation is nearly consistent with the analytical expression of RMS position error. In addition, initial orbit determination (IOD) is carried out by using the triangulation positioning data, and the results show that the IOD accuracy of two-site observation is significantly higher than that of the single-site observation.