A method of position analysis for spherical mechanisms with four-bar closed-loop chains was proposed. The mechanism was divided into a four-bar closed-loop mechanism and a single-opened-chain (SOC) unit. The constraint equation of the four-bar closed-loop was established with spherical loop equation. The constraint equation of SOC was set up with coordinate transformation and direction cosine matrix. The coupled constraint equation of whole mechanism was built up based on spherical trigonometry. The proposed method was simple to set up constraint, easy for elimination and less extraneous root, which was helpful to obtain symbolic solutions or figure-symbolic solutions. 