Star diblock dendrimers are a new class of polymeric materials. They are macromolecules with a well-defined and monodisperse (of a colloid) containing particles of uniform size), highly branched three dimensional architecture. The study of ordered and stable single star diblock dendrimers is challenging in polymer science. In this work, we use Monte Carlo simulation method to study the coarse-grained single star diblock dendrimers and the intra-/inter monomers interaction potential energies to model their complex system. In this thesis brief overviews of Monte Carlo simulation technique and basic highlights of molecular dynamics are addressed. Its less complexity of MC codes and fast equilibration of system makes simulation technique the first choice. In this thesis the effect of temperature, force (interaction potential) between inner beads, generation and dendron number on the distribution of inner and outer monomer, packing fraction, overall shape and size of single star diblock dendrimers are well studied properties. Increment of generation number determines the increment of the arm length of the single star diblock dendrimers. Therefore the radius of gyration of single star diblock dendrimers increases as the generation number increases. On the other hand, as the temperature increases then the whole molecules become expand, which causes the size of the dendrimers to increases for increasing temperature. In addition to radius of gyration the probability of finding the monomer of single star diblock dendrimers at far distance from the center increases with increasing generation and dendron number; but the distributions restricted to the vicinity of the center bead for lower generation and dendron number. Packing fraction of the dendrimers is also found to increase as the generation number increases, but packing fraction of the dendrimers decrease s as the temperature increases. Packing fraction of dendrimers is also increases as the dendron number increases and decreases as the interaction potential between beads is decreases. Finally, the structure and alignment properties of single dendrimers studied here under different parameter are demonstrated. These properties can be fine-tuned towards an intended potential applications since, this dendrimers have led to the most impressive developments and rapidly expanding areas of current science properties to design various advanced materials for biomedical applications. KEY WORDS: star shaped polymers, single diblock dendrimers, modeling of single dendrimers, Monte Carlo simulation, coarse grained model