Abstract: Viscoelastic oscillator (VEO) is a basic physical element used to characterize viscoelastic damper. To address the common drawbacks of the conventional integer derivative model of VEO, the fractional VEO considering geometric factor is proposed and its frequency response function is derived. The SFVEO, one of the representative VEOs, is adopted as the study case for investigating the frequency characteristics and parameter influence. The numerical results show that there are harmonic peaks in the amplitude-frequency response and corner frequencies in the phase-frequency response. The harmonic peaks and the corner frequencies are influenced by system parameters including natural frequency, fractional order, geometric factor and damping ratio. Natural frequency, damping ratio and geometric factor exhibit notable impact on the amplitude-frequency response at low frequency-ratio stage, while fractional order strongly affects it at high frequency-ratio stage. All parameters display evident impact on the phase-frequency response at low frequency-ratio stage. This study can provide essential theoretical references for the design and multi-object optimization of the viscoelastic damper.