In this paper, we study the problem of aircraft 4D trajectory prediction and conflict detection which is one of the key functions of the Next Generation Air Transportation System (NextGen). A stochastic linear hybrid system (SLHS) with two different discrete state transition models is proposed to describe the aircraft motion. Based on the SLHS model, a 4D trajectory prediction algorithm is proposed utilizing some prior information about the aircraft's intent. Also, a computationally efficient conflict detection algorithm is developed based on the cumulative distribution function (cdf) approximation for the quadratic form of Gaussian random variables. The performance of the proposed algorithms is validated through an illustrative air traffic scenario.