PURPOSE To develop a collimator trajectory optimization paradigm for volumetric modulated arc therapy (VMAT) and evaluate this technique in paraspinal stereotactic body radiation therapy (SBRT). METHOD AND MATERIALS We propose a novel VMAT paradigm, Coll-VMAT, which integrates collimator rotation with synchronized gantry rotation, multileaf collimator (MLC) motion, and dose-rate modulation. At each gantry angle a principal component analysis (PCA) is applied to calculate the primary cord orientation. The collimator angle is then aligned so that MLC travel is parallel to the PCA-derived direction. An in-house VMAT optimization follows the geometry-based collimator trajectory optimization to obtain the optimal MLC position and monitor units (MU) at each gantry angle. A treatment planning study of five paraspinal SBRT patients compared Coll-VMAT to standard VMAT (fixed collimator angle) and static field IMRT plans. Plan evaluation statistics included planning target volume (PTV) V95%, PTV-D95%, cord-D05%, and total beam-on time. RESULTS Variation of collimator angle in Coll-VMAT plans ranges from 26 degrees to 54 degrees , with a median of 40 degrees . Patient-averaged PTV V95% (94.6% Coll-VMAT vs. 92.1% VMAT and 93.3% IMRT) and D95% (22.5 Gy vs. 21.4 Gy and 22.0 Gy, respectively) are highest with Coll-VMAT, and cord D05% (9.8 Gy vs. 10.0 Gy and 11.7 Gy) is lowest. Total beam-on time with Coll-VMAT (5,164 MU) is comparable to standard VMAT (4,868 MU) and substantially lower than IMRT (13,283 MU). CONCLUSION Collimator trajectory optimization-based VMAT provides an additional degree of freedom that can improve target coverage and cord sparing of paraspinal SBRT plans compared with standard VMAT and IMRT approaches.