Categorization of materials such as bark, fabric, leather is an important function in object vision. These materials are characterized by specific textures that consist of complex combinations of low-level image features such as local contrast, spatial frequency and orientation, but how these complex combinations are represented in the visual system was largely unknown. In our previous study, we have reported that neurons recorded from V4 of awake monkeys respond to naturalistic textures parametrically generated by a texture synthesis algorithm (Portilla & Simoncelli, 2000) and that the tuning of these cells could be mapped in a texture space defined using the parameters of the synthesis algorithm (Okazawa et al, Neuro 2013). In the present study, we examined whether responses of these neurons can be explained by the weighted linear sum of the texture synthesis parameters. We found that the neuronal responses to hundreds of textural stimuli could be successfully fit as a linear tuning to these features. Individual neurons were tuned to relatively small number of parameters, which enabled us to visualize what particular features activated V4 neurons. We also tested the sensitivities of responses to image manipulations such as Fourier-phase randomization and found that the results could generally be explained by the tuning to the parameters. Furthermore, computational analyses showed that the observed neuronal tunings are suitable to classify textures into different material categories. These results indicate that neural selectivity to natural textures in V4 could be understood in terms of the selectivity to the collection of these image features, which gives us further insight into how we perceive materials of objects.