Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection between different approaches. In particular, whether Independent Set would be better approximable once endowed with subexponential-time or fpt-time is a central question. In this paper, we present a strong link between the linear PCP conjecture and the inapproximability, thus partially answering this question.