In this work, a terahertz (THz) fiber directional coupler with a symmetric dual-suspended core structure has been proposed for realizing low loss and polarization-insensitive coupling length in the THz frequency region. The fiber core of the directional coupler consists of two round solid dielectric rods supported by two intersecting thin dielectric layers. Numerical simulations performed using the full-vector finite element method show that a short polarization-independent coupling length can be obtained by adjusting the geometric parameters of the fiber. Moreover, a low-loss THz fiber directional coupling performance can also be achieved at a central frequency of 1.00-THz and approximately 0.16 THz of bandwidth. For example, a coupler with a length of 0.421 cm has a transmission loss of 0.30 dB and 0.26 dB for the x- and y-polarization modes, respectively.