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We investigate the properties of the focus-beamed magneto-optical trap (FBT) of Rb$^{85}$ atoms, which provides more optical accessibility in contrast to typical magneto-optical trap (MOT). We have characterized the relations between dependent variables i.e. loading time, number and density of trapped atoms versus various trap parameters, e.g. laser intensities, detuning frequency etc. In this paper, we will discuss three distinctive features of the FBT comparing to those of a standard MOT. First, the atomic density showed sudden drop at cooling intensity of 4 mW/cm$^2$ and completely vanished at 8 mW/cm$^2$. Soncond, the loading time appeared strongly dependent of the intensity of cooling beams but then developed a plateau over the magnetic field gradient greater than 15 G/cm. Third, the number of trapped atoms was found to be more sensitive to the intensity of repump beams than the cooling ones. Although the trap can capture fewer atoms comparing to the standard MOT, due to its asymmetric geometry, it offers an alternative trap configuration for preparing single atom.