The magnet design choices and calculations for HIRFL-CSR (Heavy Ion Research Facility in Lanzhou Cooling Storage Ring) are presented. CSR desires the dipole magnet field uniformity B/B-o less than or equal to +/-10(-4) and good field width reaching to +/-70 mm and +/-110 mm for the main ring and experimental ring respectively. For the dipole of CSRm, an H type was chosen with an air circle on the pole to improve the field homogeneity that was obtained with 2-D and 3-D code calculations. For CSRe, because the demand by the physics experiments, the dipole was chosen as C type. Many ideas were adopted to reduce its size, for it is very difficult to fabricate such a large laminated dipole in our country. All quadrupole lenses need field nonlinear gradient better than +/-2 x 10(-3) in the good field region which width is +/-80 mm and +/-140 mm for the main ring and experimental ring respectively. All magnets will be laminated of 0.5 mm-thick sheets of cold rolled electrical steel with an armor-coated surface.