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Free-electron lasers (FELs) are fourth-generation light sources that deliver extremely high intensity, ultrashort light pulses over a broad wavelength range from far-infrared to hard x ray. FELs based on the self-amplified spontaneous emission principle have been successfully operated with ultrahigh brightness and a broad wavelengths tuning range with good transverse coherence but poor temporal coherence. In contrast, the laser-seeded FELs have provided full coherence but at selected central wavelengths, usually the harmonics of the laser seeds, with relatively narrower tuning range. We report the experimental demonstration of a high-gain harmonic-generation (HGHG) FEL that is continuously tunable over a wide range using the combination of optical parametrical amplification, variable-gap undulator, and harmonic selection, where the temporal coherence is preserved as confirmed with the Michelson interferometry. In order to achieve higher photon energies, the first try of cascaded HGHG with a fresh-bunch technique is also made at the Shanghai Deep Ultraviolet Free-electron Laser test facility.