The modal characteristics of a Photonic-Crystal Vertical-Cavity Surface-Emitting diode Laser (PC-VCSEL) have been investigated. Photonic crystal structure, realized by a regular net of air holes within the layers, has been etched in the upper DBR mirror. An advanced three-dimensional, vectorial electromagnetic model has been applied to a phosphide - based device design featuring InGaAlAs active region, AlGaAs/GaAs mirrors and a tunnel junction to confine the current flow. For the structure under consideration a single mode operation has been found for the hole diameter over photonic crystal lattice constant ratio between 0.1 - 0.3.