Frequency is one of the most important physical quantities of electromagnetic (EM) waves. With the development of terahertz (THz) technology, high-precision measurement of THz frequency is required in THz laser development, wireless communication and ultra fine spectrum measurement. The traditional Fabry-Perot (F-P) interferometry and heterodyne detection method are both difficult to achieve high-precision measurement of THz frequency. Within the range of light wave band, the femtosecond optical frequency comb has long been applied to the light wave frequency measurement due to its extremely high accuracy and stability. By using frequency comb method, measurement with accuracy in the order of 10-11 can also be achieved in THz band. To generate THz frequency combs with stable and controllable frequency, it is required to conduct precise stabilization control on repetition frequency of the femtosecond laser. As a result, some special designs are needed for the femtosecond laser in addition to repetition frequency control devices, including the reference signal source, servo-control module, HV drive module, temperature control module, etc., resulting in a rather complicated system. In this paper, a new method for THz frequency measurement by using an unstabilized femtosecond laser is introduced. The laser is free running and the repetition frequency continuously reduces approximately 8 kHz in 6 h, which is the result of a lengthened laser cavity due to the thermal expansion caused by temperature rise after the laser has been switched on. The repetition frequency and beat signal frequency are simultaneously and continuously measured by two frequency counters. The THz frequency can be calculated from the data with accuracy in the order of 10-10. Although the measurement precision is reduced by one order compared with that obtained by using stabilized femtosecond laser, the system is greatly simplified. The femtosecond laser and complicated repetition frequency control devices no longer need to be specifically designed. This new method will greatly expand the applicable scope of the frequency comb method in measuring THz frequency.