The Gamma-Ray and AntiMatter Survey (GRAMS) is a next-generation balloon/satellite mission utilizing a Liquid Argon Time Projection Chamber (LArTPC) detector to measure both MeV gamma rays and antinuclei produced by dark matter annihilation or decay. The GRAMS can identify antihelium-3 events based on the measurements of X-rays and charged pions from the decay of the exotic atoms, Time of Flight (TOF), energy deposition, and stopping range. This paper shows the antihelium-3 sensitivity estimation using a GEANT4 Monte Carlo simulation. For the proposed long-duration balloon (LDB) flight program (35 days $ \times $ 3 flights) and future satellite mission (2-year observation / 10-year observation), the sensitivities become 1.47 $\times$ 10$^{-7}$ [m$^2$ s sr GeV/n]$^{-1}$ and 1.55 $\times$ 10$^{-9}$ [m$^2$ s sr GeV/n]$^{-1}$ / $3.10\times10^{-10}$ [m$^2$ s sr GeV/n]$^{-1}$, respectively. The results indicate that GRAMS can extensively investigate various dark matter models through the antihelium-3 measurements.