Using first-principles calculations, we designed a two-dimensional material, monolayer AgBiP2Se6, with the thickness of only 6 Å, which exhibited out-plane ferroelectricity. The ground state of the monolayer AgBiP2Se6 was not purely ferroelectric since the out-plane ferroelectricity originated from the compensated ferrielectric state: the off-centering antiparallel displacements of Ag+ and Bi3+ ions. The compensated ferrielectric ordering has superiority on reducing the depolarization field to stabilize the ferroelectricity. Furthermore, together with strong visible-light adsorption and suitable band edge alignments, we proposed the monolayer AgBiP2Se6 as a visible-light photocatalyst for water-splitting as the out-plane polarization could enhance the electron-hole separation. Our results offer a new way to overcome the critical thickness limitation of nanoscale ferroelectrics. The out-plane ferroelectricity in monolayer AgBiP2Se6 has great potential for developing various devices with desirable applications.