The paper gives an answer to the question: if the maritime area of Croatia (territorial sea and continental shelf) is involved, which is the best Lambert conic conformal map projection for the territory of Croatia? Numerical realization demanded the northernmost and the southernmost coordinates on the land and sea of Croatia. Since the coordinates of the southernmost point on the sea, i.e. those on the line of the continental shelf, had never been calculated before, it had to be done in this work. Thereafter eight variants of conic conformal map projections with respect to the distribution of linear distortions were analyzed. Each variant was clearly defined, and they differ in the constants of projection which were obtained by setting initial conditions. On the basis of performed research the best Lambert conic conformal map projection for the territory of Croatia including its territorial sea and continental shelf was proposed.