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In a thin Weyl semimetal, a thickness dependent Weyl-orbit quantum oscillation was proposed to exist, originating from a nonlocal cyclotron orbit via electron tunnelings between top and bottom Fermi-arc surface states. Here, magneto-transport measurements were carried out on untwinned Weyl metal SrRuO3 thin films. In particular, quantum oscillations with a frequency Fs1 ≈ 30 T were identified, corresponding to a small Fermi pocket with a light effective mass. Its oscillation amplitude appears to be at maximum for thicknesses in a range of 10 to 20 nm, and the phase of oscillation exhibits a systematic change with film thickness. The constructed Landau fan diagram shows an unusual concave downward curvature in the 1/μ0Hn-n curve, where n is the Landau level index. From thickness and field-orientation dependence, the Fs1 oscillation is attributed to be of surface origin. Those findings can be understood within the framework of the Weyl-orbit quantum oscillation effect with non-adiabatic corrections. [ABSTRACT FROM AUTHOR]