Embodiments of the invention relate to a spatial stereoscopic display device and an operating method thereof. The spatial stereoscopic display device comprises: a laser source; a two-dimensional scanning unit, receiving and projecting the laser light onto a variable isoclinic transflective unit; the variable isoclinic transflective unit, receiving and dividing the laser light into a first and second splitting lights intersecting in an imaging space, by transmission and reflection; a power source and position sensor unit, connected with the variable isoclinic transflective unit to control an intersection of the first and second splitting lights in the imaging space; the imaging space, provided with an up-conversion material inside, and the up-conversion material at the intersection of the first and second splitting lights is excited to form a light-emitting point; and the 3D modulator, connected with the laser source, the two-dimensional scanning unit, the power source and position sensor unit.