Energy detection is a reliable non-coherent signal processing technology of spectrum sensing of cognitive radio networks, which thanks to its low complexity, no requirement of priori received information and fast sensing ability etc. Since the excellent performance of energy detection would be actually affected by physical multipath fading, this paper is concentrating on characteristics analysis of energy detection over composite shadowed fading channels. The small-scale and line-of-sight fading distribution consists of particular examples such as Rayleigh, Hoyt, Nakagami-m and one sided Gaussian distributions. Based on this, we derive the probability density function of signal envelope and signal-to-noise ratio of the composite shadowed fading channels, which could accurately present the line-of-sight shadowed fading characterization. Subsequently the exact close-form expressions with infinite series formulation for the appropriate detection probability have been firstly extended to estimate detection capacity of the above-mentioned model by adopting Inverse Gaussian asymptotic distribution. In addition, the absolute truncation error is deduced for evaluating minimum detection efficiency. The established model can be also applied in detection estimation with non-integral fading parameters. Last but not least, the analytical results and quantification performance are approved by numerically evaluation with MATHEMATICA and MATLAB as the power variables of dominant components changes.