A numerical solution for the broadband planar-lightwave-circuit (PLC) splitter with a variable splitting ratio based on asymmetric three waveguides weighted by the Blackman weighting function is designed for passive optical network applications with wavelengths between 1.53 and 1.57 μm. The performance of the proposed splitter is verified using the beam propagation method (BPM). It was found that a polynomial function of the splitting ratios accompanying a geometrical shift can be derived from the proposed splitter. The splitting ratio can be changed from 50:50 to 90:10 with this geometrical shift. The excess loss, crosstalk, polarization dependent loss, and splitting ratio variations against wavelength of the proposed splitter with wavelengths between 1.53 and 1.57 μm are better than 0.139 dB, -22.75 dB, 0.006 dB, and 0.335%, respectively. Obviously, the proposed splitter with variable splitting ratio retains the advantages of the symmetric design, such as low excess loss, low crosstalk, polarization insensitivity, broadband, and wavelength insensitivity.