Intrinsic triferroicity is essential and highly sought for novel device applications, such as high-density multistate data storage. So far, the intrinsic triferroicity has only been discussed in three-dimensional systems. Herein on basis of first-principles, we report the intrinsic triferroicity in two-dimensional lattice. Being exfoliatable from the layered bulk, single-layer FeO2H is shown to be an intrinsically triferroic semiconductor, presenting antiferromagnetism, ferroelasticity and ferroelectricity simultaneously. Moreover, the directional control of its ferroelectric polarization is achievable by 90° reversible ferroelastic switching. In addition, single-layer FeO2H is identified to harbor in-plane piezoelectric effect. The unveiled phenomena and mechanism of triferroics in this two-dimensional system not only broaden the scientific and technological impact of triferroics but also enable a wide range of nanodevice applications.