An installation structure of countertop faucet includes a base having an insertion section extending through a mounting hole formed in a counter to engage a locking nut to be secured. The insertion section has a top end forming a receiving bore of which a circumferential wall forming two positioning holes communicating with the receiving bore. Each positioning hole receives therein a releasing module. The bottom of the base forms two water inlet passages communicating with the receiving bore and receiving stop valves therein and coupled to couplers for connection with water inlet tubes. A faucet has a joint section received in the receiving bore and having water guide tubes fit into the water inlet passages. The joint section forms two receiving apertures receiving therein positioning modules respectively engageable with the positioning holes to fix the faucet and being released by the releasing module to detach the faucet from the base.