Planets are born in the mid-plane of accretion discs around young protostars. This process takes place most likely in weakly ionised regions, where the evolution of the environment is driven by internal turbulence and the gas flow is not laminar but has stochastic components. Turbulence can be generated purely hydrodynamically via different instabilities, like the vertical shear instability (VSI). A fast pathway to the formation of giant planetary cores has been recently identified in pebble accretion, though a realistic investigation of this process in a turbulent environment was necessary. We tested the solid accretion of a large range of dust sizes on to different planetary core masses in a VSI turbulent global 3D disc and compared it with a laminar disc. Furthermore, we tested the influence of a realistic equation of state and radiative cooling on the efficiency of pebble accretion. We found that turbulence decreases slightly the solid accretion efficiency with respect to analytical calculations of laminar discs, having a ~2% efficiency of pebble-like particles for a 5 Earth-mass planet at 5 au. The introduction of radiative transfer can affect this result significantly by changing the aspect ratio of the disc, thus the pebble isolation mass.