RNA (ribonucleic acids) tertiary (3D) structure prediction is crucial for understanding the relationship between RNA structures and their functions. RNA 3D structure prediction remains challenging in spite of advancements in recent years. In this thesis, we propose a new method for RNA 3D structure prediction with a novel mathematical model. We model an RNA 3D structure as a collection of interacting helixes with a succinct geometric characterization for every pair of consecutive nucleotides on the RNA sequence. Given a small set of parameters, such as various angles between segments, the model geometrically projects any consecutive segment of the RNA sequence into a single helix in the 3D space, enabling effective assembly of RNA 3D structure. Tests on RNA sequences from the Protein Data Bank have shown the success of our method on prediction of 3D structures involving double-helices, hairpin loops, and bulges.