Two-dimensional parametrized surfaces immersed in the su (N) algebra are investigated. The focus is on surfaces parametrized by solutions of the equations for the CP(N-1) sigma model. The Lie-point symmetries of the CP(N-1) model are computed for arbitrary N. The Weierstrass formula for immersion is determined and an explicit formula for a moving frame on a surface is constructed. This allows us to determine the structural equations and geometrical properties of surfaces in R(N2-1). The fundamental forms, Gaussian and mean curvatures, Willmore functional and topological charge of surfaces are given explicitly in terms of any holomorphic solution of the CP(2) model. The approach is illustrated through several examples, including surfaces immersed in low-dimensional su(N) algebras.