Recently, monoclinic-phase GaTe has attracted much attention due to its potential applications in nanoelectronics. Despite the experimental research, theoretical studies on the thermal and transport properties, which are necessary to provide information for future applications, are still absent. We have systematically investigated the electronic, phonon and electron transporting, and thermoelectric properties of monolayer and bulk GaTe using first-principles calculations plus the Boltzmann transport equation. At the valence band maximum and conduction band minimum, the effective mass shows large anisotropy as the band dispersions are along different k-paths. The group velocity of acoustic modes also shows large anisotropy owing to the in-plane low-symmetry. Our calculations reveal that the in-plane thermal conductivities, κa and κb, take 3.5 and 8.9 W m-1 K-1, respectively, for the bulk at 300 K, compared to κa = 5.5 and κb = 10.4 W m-1 K-1 of the monolayer. Due to the van der Waals interactions between interlayers, the out-of-plane thermal conductivity is very small, κc = 1.8 W m-1 K-1. The difference between the in-plane thermal conductivities of the bulk and the monolayer can be attributed to the strengthened Umklapp scattering, which is caused by the stiffening of the lowest-frequency optical mode in the bulk. The hole mobilities of the bulk is found to be about 12-35 cm2 V-1 s-1 at 300 K, in good agreement with the experimental results. The monolayer is found to have smaller mobility but larger anisotropy than those of the bulk. Interestingly, the out-of-plane conductivity is anomalously larger than the in-plane one for the bulk, which is attributed to the orbital overlaps between the interlayer Te atoms. Moreover, n-type GaTe is found to have much larger mobility and anisotropy than the p-type one, which is useful for future applications. Compared with the case of monolayer GaTe, thermoelectric performance can be enhanced by one order of magnitude for the bulk GaTe by exploiting the out-of-plane thermal and electrical conductivities.