An arbitrary optical frequency synthesizer with a broad tuning range and high frequency accuracy is presented. The system includes an external cavity diode laser (ECDL) as the output laser, an Erbium-doped optical frequency comb being a frequency reference, and a control module. The optical frequency from the synthesizer can be continuously tuned by the large-scale trans-tooth switch and the fine intra-tooth adjustment. Robust feedback control by regulating the current and PZT voltage enables the ECDL to phase-lock to the Erbium-doped optical frequency comb, therefore to keep stable frequency output. In the meanwhile, the absolute frequency of the synthesizer is determined by the repetition rate, the offset frequency and the beat frequency. All the phase lock loops in the system are traced back to a Rubidium clock. A powerful and friendly software is developed to make the operation convenient by integrating the functions of frequency setting, tuning, tracing, locking and measuring into a LabVIEW interface. The output frequency tuning span and the uncertainty of the system are evaluated as >6 THz and <3 kHz, respectively. The arbitrary optical frequency synthesizer will be a versatile tool in diverse applications, such as synthetic wavelength based absolute distance measurement and frequency-stabilized Cavity Ring-Down Spectroscopy.