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It is discussed that the point spread function (PSF) of multiplexing parallel beam (MPB) is shift-invariant; the spatial resolution is linear as a function of depth h and the geometrical sensitivity is converged to a constant value at far field, by using Monte Carlo simulation in this work. The results indicate that the MPB collimator may maintain the same system characteristics as parallel beam (PB) collimator. Although the minimum standard deviation (SD) of MPB is more 3.7% than the PB with high sensitivity (HSPB), the improved resolution is 55.2% at h=160mm, compared with HSPB in this work. The reconstruction process also indicates that the convergence rate of MPB is slower than the HSPB because the projection counts are part of overlapping and the PSF of oblique PB (OPB) is asymmetrical. However the effective hole length is used in the calculation of the system matrix to correct for the penetration, which has a satisfactory result. From a visual assessment, the reconstructed image may well satisfy clinical criteria and it is therefore worth investigating this novel MPB collimator system for clinical imaging.