Here we report the preparation and superconductivity of the 133-type Cr-based quasi-one-dimensional (Q1D) RbCr3As3 single crystals. The samples were prepared by the deintercalation of Rb+ ions from the 233-type Rb2Cr3As3 crystals which were grown from a high-temperature solution growth method. The RbCr3As3 compound crystallizes in a centrosymmetric structure with the space group of P63/m (No. 176) different with its non-centrosymmetric Rb2Cr3As3 superconducting precursor, and the refined lattice parameters are a = 9.373(3) {AA} and c = 4.203(7) {AA}. Electrical resistivity and magnetic susceptibility characterizations reveal the occurrence of superconductivity with an interestingly higher onset Tc of 7.3 K than other Cr-based superconductors, and a high upper critical field Hc2(0) near 70 T in this 133-type RbCr3As3 crystals.