To determine the geolocation of a pixel for spaceborne synthetic aperture radar (SAR) images, traditional indirect geolocation methods can cause great computational complexity. In this paper, a fast, three-dimensional, indirect geolocation method without ground control points (GCPs) is presented. First, the Range-Doppler (RD) geolocation model with all the equations in the Earth-centered rotating (ECR) coordinate system is introduced. By using an iterative analytical geolocation method (IAGM), the corner point locations of a quadrangle SAR image on the Earth’s surface are obtained. Then, a three-dimensional (3D) grid can be built by utilizing the digital surface model (DSM) data in this quadrangle. Through the proportional relationship for every pixel in the 3D grid, the azimuth time can be estimated, which is the key to decreasing the calculation time of the Doppler centroid. The results show that the proposed method is about 12 times faster than the traditional method, and that it maintains geolocation accuracy. After acquiring the precise azimuth time, it is easy to obtain the range location. Therefore, the spaceborne SAR image can be geolocated to the Earth surface precisely based on the high-resolution DSM data.