Accurate distances to supernova remnants (SNRs) are crucial in determining their size, age, luminosity and evolutionary state. To determine distances, 34 bright SNRs were chosen from the VLA Galactic Plane Survey (VGPS) to extract HI absorption spectra. Analyzing the HI absorption and 13CO emission spectra, HI and 13CO channel maps, distances to the 34 SNRs were calculated. To estimate a distance, an accurate rotation curve is essential in order to obtain orbital velocities V(R). The orbital velocities obtained by the tangent point method were compared with the Universal Rotation Curve as a test of its validity. From the analysis 12 new, 9 changed, 6 revised and 7 confirmed distances are presented. Furthermore, the selection effects of the study sample is discussed. The surface density of SNRs were calculated and found to be proportional to the density of stars. The validity of the Σ-D relation of estimating distances is discussed.