The transport properties of a paired Majorana bound states (MBSs) in a parallel junction are theoretically investigated, by considering the influence of different MBS-lead coupling manners, i.e., left-right asymmetric coupling, upper-down asymmetric coupling, and left-right upper-down asymmetric coupling. The calculation results show that the MBS-lead coupling manners affect the transport properties in a substantial way. For the former two configurations, the shot noise Fano factor in the zero-bias limit is related to the value of the conductance maximum with F0=1+12Tmax (conductance G=e2hT). When both the left-right and upper-down symmetries are broken, such a relation is modified into F0=1-12T0. These results will be helpful for describing the transport characteristics of the junction with MBSs. [ABSTRACT FROM AUTHOR]