In recent years, semimetals have aroused people's research interest. Here, we systematically study phonon and electronic transport properties of the ZrBeSi with semimetal character by using the first-principles calculations together with the Boltzmann transport theory. Calculated lattice thermal conductivities of the ZrBeSi along a and c axes are 31.3 W/m· K and 56.0 W/m· K at room temperature, respectively, which are larger than the most semiconductors and semimetals. By comparing with other semimetals, we find that the larger lattice thermal conductivity of ZrBeSi is due to its smaller Grüneisen parameter, which indicates the weaker phonon scattering. Main contributions to the lattice thermal conductivities along a and c axis come from the acoustic branches, and conversely, the contributions of optical branches are very small. In addition, we calculate the Seebeck coefficient and the electron thermal conductivity of ZrBeSi based on the relaxation time approximation. The electronic transport properties of ZrBeSi exhibit strong anisotropy in both a and b directions. Calculated electronic thermal conductivities of pristine ZrBeSi along a and c axes are 8.8 W/m· K and 9.7 W/m· K at room temperature, respectively. Furthermore, we also obtain the figure of merit (ZT) on the basis of phonon and electron transport. The obtained ZT along c axis reaches a maximum of 0.11 at 900 K, demonstrating that ZrBeSi has a general ZT, but it has good heat conduction ability. Our research will help to understand the transport properties of semimetals and expand the application of semimetals to heat conduction devices. At the same time, it also provides some reference for the future experimental work.