We report the first theoretical characterization of the pressure-dependence of hydrogen abstraction from methyl formate (MF) by a hydroxyl radical (OH) at combustion, atmospheric and interstellar temperatures. The reaction kinetics of MF + OH over a broad temperature range of 20-2000 K were studied using Rice-Ramsperger-Kassel-Marcus/master equation (RRKM/ME) theory. The M06-2x/ma-TZVP density functional method was adopted to construct the potential energy surface. The multi-structural torsional (MS-T) method was employed to account for the multi-conformer and torsional coupling effects. The barrier-less entrance channel forming an H-bonded complex was treated by phase state theory using long-range isotropic potential. The inner channel converting the complex into products was treated by both transition state theory and variational transition state theory in conjunction with asymmetric Eckart tunneling. We calculated the rate coefficients at the high-pressure and low-pressure limits, as well as by the pre-equilibrium model (PEM). The rate coefficients at 20-2000 K and 0.001-100 bar were determined and compared with the previous experimental results. Our calculations show a fairly good agreement with the measurements at 22-1344 K: a small deviation of <25% at combustion temperatures and a factor of 1.5-2.2 at interstellar temperatures. Besides providing an improved rate coefficient determination at combustion temperatures, we elucidate the pressure-dependence of the rate coefficient at atmospheric and interstellar temperatures.