First-passage probability estimation of stochastic dynamic systems is an important but still challenging problem in various science and engineering fields. This paper proposes a novel parametric approach, termed 'fractional moments-based mixture distribution' (FMs-MD), to address this challenge. Such method is based on capturing the extreme value distribution (EVD) of the studied stochastic system response in the first place. The concept of FM is then introduced to characterize the EVD, which is by definition a multi- (high-) dimensional integration. To efficiently evaluate the FM, a parallel adaptive strategy is developed by applying a sequential sampling technique, namely, refined Latinized stratified sampling (RLSS). By taking advantage of RLSS, both variance-reduction and parallel computing are possible in the process of FM computation. From the knowledge of low-order FMs, the EVD is then intended to be reconstructed. One flexible MD model is proposed on the basis of the extended Lognormal and generalized inverse Gaussian distributions. By fitting a set of FMs, the EVD can be reconstructed via this mixture model. The performance of the proposed method is verified by a numerical example consisting of a Duffing oscillator with random parameters under Gaussian white noise.