The coefficient of loss and dispersion relation of a hollowcore Bragg fiber with cobwebby cladding in the THz band was investigated analytically by adjustable boundary conditions Fourier decomposition method (ABCFDM). The spectra and waveforms for three THz transmitted pulses were calculated through the hollowcore Bragg fiber. The analytical result shows that loss characteristic of the hollowcore Bragg fiber is similar to a highpass filter with variable cutoff frequency and phaseshift constant. Fiber core radius and transmission distance determinate the cutoff frequency of the highpass filters jointly. The hollowcore Bragg fiber only attenuates the THz wave in the band below the cutoff frequency, and significant phaseshift will be yield near the cutoff frequency when the THz pulse pass through the fiber. If the core radius is advisable, THz pulse will be transmitted through the hollowcore Bragg fiber effectively for a short distance.