Since the discovery of high-temperature superconductivity in cuprates, finding more unconventional superconductors and understanding their superconducting pairing mechanism has been an important theme in condensed matter physics. Recently, ternary Cr-based superconductors A2Cr3As3 (A=K, Rb, Cs) and ACr3As3 (A=K, Rb) were reported, which own quasi-one-dimensional crystal structure, containing[(Cr3As3)-] linear chains. A2Cr3As3 belongs to P6m2 space group, and ACr3As3 crystallizes in a centrosymmetric structure with the space group P63/m. Many experiments, such as nuclear magnetic resonance, London penetration depth, show that A2Cr3As3 is an unconventional superconductor. However, these A2Cr3As3 compounds are extremely unstable in air. Here, we study the superconducting gap of the air-stable RbCr3As3 single crystal, using ultralow-temperature thermal conductivity measurement. The resistivity of RbCr3As3 single crystal shows a superconducting transition temperature Tczero at 6.6 K. The normal-state resistivity data from 20 K to 8 K are fitted to (T)=0 + AT2, which gives a residual resistivity of 0=781 cm. Then, the thermal conductivity of RbCr3As3 single crystal is measured at temperature down to 80 mK and in magnetic fields up to 9 T. In zero field, residual linear term 0/T=7.5 WK-2cm-1 is observed, which is about 24% of its normal-state value, suggesting nodes in the superconducting gap. At low field, the 0/T of RbCr3As3 shows a relatively faster field dependence than single-gap s-wave superconductors. These results reveal that RbCr3As3 is likely an unconventional superconductor with superconducting gap nodes, although the exact superconducting gap symmetry and structure for this quasi-one-dimensional superconductor needs further investigation.