Poly-L-lysine (PLL) dendrimers are promising systems for biomedical applications due to their biocompatibility. These dendrimers have a specific topology: two spacers of different lengths come out of each branching point and thus the branching is asymmetric. Because of this asymmetry terminal groups are located at branches of different lengths, unlike dendrimers with a symmetric branching. This paper presents the results of the first systematic molecular dynamics simulation of such asymmetric PLL dendrimers. It is shown that PLL dendrimers are porous molecules with all terminal groups equally accessible to water. We have found that in spite of an asymmetry of branching the general structural characteristics of PLL dendrimers are rather similar to those of dendrimers with symmetric branching. We have also found that the structural characteristics of PLL dendrimers obey the general laws for dendrimers and that their electrostatic properties agree with the predictions of a general analytic theory.