Co-Pt-P ͑ϳ20 atom % Pt, ϳ3 atom % P͒ alloy films with thickness from 125 to 1000 nm have been grown by electrodeposition under constant current on a ͑100͒ oriented Cu seed layer. The influence of deposition current density and film thickness on their chemical composition, growth morphology, and structural and magnetic properties have been investigated. Co-Pt-P films consist of a fcc phase with ͑100͒ and ͑111͒ preferential orientations and a variable amount of hcp phase with ͑00.2͒ orientation, which increases with increasing current density. Grain size decreases with increasing current density. At high current density, the films exhibit significant perpendicular anisotropy and hard magnetic properties in the out-of-plane direction, with coercivity up to 3.7 kOe ͑295 kA/m͒.