The present disclosure discloses a solving method and system for an Euler angle attitude. The solving method includes: acquiring a rough rotation angle ΔT of a tool surface of a drilling tool in a search interval; performing calculation according to the rough rotation angle ΔT to obtain a variation range RangeT of the tool surface; disposing a plurality of particles within the variation range RangeT, corresponding position coordinates of the particles to an Euler angle value, randomly generating initial speeds of the particles, calculating a fitness function of each particle, and selecting the particle with the minimum fitness function as an optimal particle; updating a speed and a position of each particle, and gradually moving the particles closer to an optimal position by adopting an iteration method; and after performing n iterations until the precision of the fitness function of the optimal particle reaches a threshold.