This paper reports on the solution structure of a parallel-stranded G-quadruplex formed by the Tetrahymena telomeric sequence d(T-T-G-G-G-G-T) whose NMR parameters in potassium cation containing solution were previously published from our laboratory. The structure was determined by combining a quantitative analysis of the NMR data with molecular dynamics calculations including relaxation matrix refinement. The combined NMR-computational approach yielded a set of seven distance-refined structures with pairwise RMSDs ranging from 0.66 to 1.30 A for the central G-G-G-G tetranucleotide segment. Four of the seven structures were refined further using complete relaxation-matrix calculations to yield solution structures with pairwise RMSDs ranging from 0.64 to 1.04 A for the same tetranucleotide segment. The R-factors also decreased on proceeding from the distance-refined to relaxation matrix-refined structures. The four strands of the G-quadruplex are aligned in parallel and are related by a 4-fold symmetry axis coincident with the helix axis. Individual guanines from each strand form planar G.G.G.G tetrad arrangements with each tetrad stabilized by eight hydrogen bonds involving the Watson-Crick and Hoogsteen edges of the guanine bases. All guanines adopt anti glycosidic torsion angles and S type sugar puckers in this right-handed parallel-stranded G-quadruplex structure. The four G.G.G.G tetrad planes stack on each other with minimal overlap of adjacent guanine base planes within individual strands. The thymine residues are under-defined in the solution structure of the d(T-T-G-G-G-G-T) G-quadruplex and sample amongst multiple conformations in solution.