In this study we performed magnetic, mechanical and thermal modeling of a 3T actively shielded whole body MRI (Magnetic Resonance Imaging) magnet. The final design had an overall magnet length and conductor length which can lead to conduction cooled designs which are comparable to NbTi helium bath cooled 3 T designs. The design had a magnetic field homogeneity better than 10 ppm (part-per-million) within a DSV (Diameter of Spherical Volume) of 49 cm. A new class of MgB2 strand especially designed for MRI applications was considered as a possible candidate for winding such magnets. The magnet design was a segmented coil type optimized to minimize conductor length while hitting the standard field quality and DSV specifications as well as a standard, compact size 3 T system. Unlike the frequently used Helmholtz-like coil pair design (even number of coils, typically 8 or 10 coils in total) we used a Maxwell-like configuration (an odd number of coils, containing 9 coils in total). This Maxwell-like coil design is advantageous for a number of reasons, in particular because it can allow a higher inner winding diameter in the central part of the MRI magnet. The final design achieved 3 T in the bore, with 10 ppm homogeneity in a 49 cm DSV. The total magnet length is 1.37 m, and the total conductor length is 121 km. The operational current is 287 A, and based on a 4.2 K Ic = 383 A, this gives I/Ic = 0.75. This work represents the first magnetic design for a whole-body 3 T MgB2-based MRI magnet for a short (1.37 m length) magnet which uses the performance parameters of existing MgB2 wire. This result represents a strong step towards a viable 3 T, whole body, conduction cooled MRI based on MgB2 conductor.