We report measurements of the upper critical field Hc2 as functions of temperature T , polar angle θ (of the field direction with respect to the crystallographic c axis), and azimuthal angle φ (of the field direction relative to the a axis within the ab plane) for the Cr-based superconductor K2Cr3As3 with a quasi-one-dimensional and non-centrosymmetric crystal structure. We confirm that the anisotropy in Hc2(T ) becomes inverse with decreasing temperature. At low temperatures, Hc2(θ) data are featured by two maxima at θ = 0 (H c) and π/2 (H⊥c), which can be quantitatively understood only if uniaxial effective-mass anisotropy and absence of Pauli paramagnetic effect for H⊥c are taken simultaneously into consideration. The in-plane Hc2(φ) profile shows a unique threefold modulation especially at low temperatures. Overall, the characteristic of the Hc2(θ, φ, T ) data mostly resemble those of the heavy-fermion superconductor UPt3, and we argue a dominant spin-triplet superconductivity with odd parity in K2Cr3As3.