We present cosmological constraints based on the cosmic microwave background (CMB) lensing potential power spectrum measurement from the recent 500 deg 2 SPTpol survey, the most precise CMB lensing measurement from the ground to date. We fit a flat ΛCDM model to the reconstructed lensing power spectrum alone and in addition with other data sets: baryon acoustic oscillations (BAO) as well as primary CMB spectra from Planck and SPTpol. The cosmological constraints based on SPTpol and Planck lensing band powers are in good agreement when analysed alone and in combination with Planck full-sky primary CMB data. Within the ΛCDM model, CMB lensing data are primarily sensitive to the amount of large-scale structure as parametrized by σ 8 Ω 0.25 m . With weak priors on the baryon density and other parameters, the SPTpol CMB lensing data alone provide a 4% constraint on σ 8 Ω 0.25 m = 0.593 ± 0.025. Jointly fitting with BAO data, we find σ 8 = 0.779 ± 0.023, Ω m = 0.368 +0.032 −0.037 , and H 0 = 72.0 +2.1 −2.5 km s −1 Mpc −1 , up to 2 σ away from the central values preferred by Planck lensing + BAO. However, we recover good agreement between SPTpol and Planck when restricting the analysis to similar scales. We also consider single-parameter extensions to the flat ΛCDM model. In combination with Planck primary CMB measurements and BAO, the SPTpol lensing spectrum constrains the spatial curvature to be Ω K = −0.0007 ± 0.0025 and the sum of the neutrino masses to be m ν < 0.23 eV at 95% C.L., both in good agreement with the full-sky Planck lensing results. With the differences in the S/N of the lensing modes and the angular scales covered in the lensing spectra, this analysis represents an important independent check on the full-sky Planck lensing measurement.