Digital signal processing requires digital filters with variable frequency characteristics. A variable digital filter (VDF) is a filter whose frequency characteristics can be easily and instantaneously changed. In this paper, we present a design method for variable linear-phase finite impulse response (FIR) filters with multiple variable factors and a reduction method for the number of polynomial coefficients. The obtained filter has a high piecewise attenuation in the stopband. The stopband edge and the position and magnitude of the high piecewise stopband attenuation can be varied by changing some parameters. Variable parameters are normalized in this paper. An optimization methodology known as semidefinite programming (SDP) is used to design the filter. In addition, we present that the proposed VDF can be implemented using the Farrow structure, which suitable for real time signal processing. The usefulness of the proposed filter is demonstrated through examples.