RV6Sn6 (R = Sc, Y, or rare earth) is a new family of kagome metals that have a similar vanadium structural motif as AV3Sb5 (A = K, Rb, Cs) compounds. Unlike AV3Sb5, ScV6Sn6 is the only compound among the series of RV6Sn6 that displays a charge density wave (CDW) order at ambient pressure, yet it shows no superconductivity (SC) at low temperatures. Here, we perform a high-pressure transport study on the ScV6Sn6 single crystal to track the evolutions of the CDW transition and to explore possible SC. In contrast to AV3Sb5 compounds, the CDW order of ScV6Sn6 can be suppressed completely by a pressure of about 2.4 GPa, but no SC is detected down to 40 mK at 2.35 GPa and 1.5 K up to 11 GPa. Moreover, we observed that the resistivity anomaly around the CDW transition undergoes an obvious change at ~2.04 GPa before it vanishes completely. The present work highlights a distinct relationship between CDW and SC in ScV6Sn6 in comparison with the well-studied AV3Sb5.