K2Cr3As3 is a newly discovered quasi-1D superconductor with a T c = 6.1 K and an upper critical field µ 0 H c2(0) ≈ 40 T three times larger than the Pauli paramagnetic limit µ 0 H p that is suggestive of a spin-triplet Cooper pairing. In this paper, we have investigated the effects of hydrostatic pressure on its T c and µ 0 H c2 by measuring the ac magnetic susceptibility χ'(T) under magnetic fields at various hydrostatic pressures up to 7.5 GPa. The major findings include: (1) T c is suppressed gradually to below 2 K at 7.5 GPa; (2) the estimated µ 0 H c2(0) decreases dramatically to below µ 0 H p above ~2 GPa and becomes slight lower than the orbital limiting field [Formula: see text] estimated from the initial slope of upper critical field via [Formula: see text] = -0.73T cdH c2/[Formula: see text] in the clean limit; (3) the estimated Maki parameter α = √2[Formula: see text]/H p drops from 4 at ambient pressure to well below 1 at P > 2 GPa, suggesting the crossover from Pauli paramagnetic limiting to orbital limiting in the pair breaking process upon increasing pressure. These observations suggested that the application of hydrostatic pressure could drive K2Cr3As3 away from the ferromagnetic instability and lead to a breakdown of the spin-triplet pairing channel. We have also made a side-by-side comparison and discussed the distinct effects of chemical and physical pressures on the superconducting properties of K2Cr3As3.