Geminga is a nearby (250 pc) middle-aged (spin-down time scale ~12,000 years) pulsar associated with a supernova remnant. Geminga has been a prime candidate for the origin of the unexpectedly high flux of cosmic-ray positrons above 10 GeV detected at Earth. Extended TeV gamma-ray emission from a 2-degree region around the Geminga pulsar was detected by the HAWC observatory, thus suggesting efficient, high-energy leptonic acceleration. Fermi-LAT observations show that the density of GeV leptons in the TeV nebula is lower than predicted by single zone and two zone diffusion models constrained with the HAWC measurements. However, the energy gap between Fermi-LAT and HAWC (~500 GeV to ~1 TeV) remains under-examined. The VERITAS gamma-ray observatory is sensitive in the energy range from 100 GeV to greater than 30 TeV, filling the gap between Fermi-LAT and HAWC. Therefore, VERITAS measurements potentially provide missing information. VERITAS has observed Geminga for 93 hours since 2009 including 28 hours in the 2018/2019 season. However, the standard VERITAS data analysis techniques have insufficient sensitivity to sources extended at the scale of the HAWC detection, due to difficulties with background estimation. We developed the Matched Runs Method (MRM) for VERITAS analysis of spatially extended sources. MRM has been demonstrated to be an effective technique by applying it to archival VERITAS data, and we are currently applying it to the Geminga observations. Here we present the summary of the MRM.