The problem of variable selection is considered in partially linear varying coefficient spatial autoregressive model. By combining profile quasi-maximum likelihood method and a class of non-convex penalty function, a variable selection method is proposed to simultaneously select important explanatory variables in parametric component of the partially linear varying coefficient spatial autoregressive model and estimate the corresponding nonzero parameters. Extensive simulation studies show that the proposed variable selection method is of satisfactory finite sample performance. Especially, the proposed variable selection method is quite robust to degree of sparseness of spatial weight matrix, intensity of spatial dependence, degree of complexity of coefficient function and non-normality of error distribution, and even works well in the case where correlation among explanatory variables is strong or number of unimportant explanatory variables is large provided that appropriate penalty function is used and sample size is moderately large. As an illustrative example, the proposed variable selection method is applied to analyze the popular Boston housing price data.