The subject of the work is a microstructure of a composite which consists of a continuum matrix and a set of isolated particles homogeneously distributed inside the matrix. It is assumed that the reinforcing particles have ellipsoidal shapes, while distribution and orientation are random. The main point of the work is a new computationally-efficient algorithm to generate microstructure of such a composite. In the algorithm the existing "concurrent" method based on an overlap elimination is extended to ellipsoidal shapes of the particles. It begins with randomly distributed and randomly oriented ellipsoidal particles which can overlap each other. During the performance of the algorithm intersections between particles are allowed and at each step the volumes of intersections are minimized by moving the particles. The movement is defined for each pair of particles based on the volume of the intersection: if two particles are overlapped, then the reference point inside the intersection is chosen and then two particles are moved in such a way that the reference point becomes the tangent point for both particles. To define the relative configuration of two particles (separate, tangent or overlapping) and to choose reference point inside the intersection volume the technique based on formulating the problem in four dimensions and then analyzing the roots of the characteristic equation are applied. The algorithm is able to generate close packed microstructures containing arbitrary ellipsoids including prolate and oblate ellipsoids with high aspect ratios (more than 10). The generated packings have a uniform distribution of orientations.