In this Letter we discuss our approach that makes possible creation of the steady-state ultracold plasma having various densities and temperatures by means of continuous two-step optical excitation of calcium atoms in the magneto-optical trap. A strongly coupled ultracold plasma can be used as an excellent test platform for studying many-body interactions associated with various plasma phenomena. The parameters of the plasma are studied using laser-induced fluorescence of calcium ions. The experimental results are well described by a simple theoretical model involving equilibration of the continuous source of charged particles by the hydrodynamical ion outflux and three-body recombination. The ultracold plasma with the peak ion density of 2.7×10^{6} cm^{-3} and the minimum electron temperature near 2 K has been prepared. Our steady-state approach in combination with the strong magnetic confinement of the plasma will make it possible to reach extremely strong coupling in such system.