Direct growth of vertically aligned carbon nanotube (CNT) arrays on substrates requires the deposition of an aluminum oxide buffer (AOB) layer to prevent the diffusion and coalescence of catalyst nanoparticles. Although AOB layers can be readily created on flat substrates using a variety of physical and chemical methods, the preparation of AOB layers on substrates with highly curved surfaces remains challenging. Here, we report a new solution-based method for preparing uniform layers of AOB on highly curved surfaces by the chemical bath deposition of basic aluminum sulfate and annealing. We show that the thickness of AOB layer can be increased by extending the immersion time of a substrate in the chemical bath, following the classical Johnson-Mehl-Avrami-Kolmogorov crystallization kinetics. The increase of AOB thickness in turn leads to the increase of CNT length and the reduction of CNT curviness. Using this method, we have successfully synthesized dense aligned CNT arrays of micrometers in length on substrates with highly curved surfaces including glass fibers, stainless steel mesh, and porous ceramic foam.