Magnetic resonance imaging (MRI) has been a primary diagnostic technique due to its high imaging quality, noninvasion and non-radiation capacity. However, the application of conventional whole body MRI is restricted by its massive size, high installation and management cost. Dedicated MRI overcomes the shortcomings of whole body MRI and has great importance in medical diagnosis. The challenge is that the design of superconducting magnet for extremity MRI is largely constrained by physiological structure of human body. As a result, a limited longitudinal length with high field homogeneity in a 160 mm diameter sphere volume (DSV) is required for superconducting magnet of extremity MRI. In this article, a non-shielded 1.5 T extremity dedicated superconducting magnet is designed by using both 0-1 integer programming and genetic algorithm and fabricated with a comprehensive consideration of superconductivity wire consumption, central magnetic field intensity and imaging region homogeneity. The NbTi superconducting wire is chosen for coil winding, and copper-to-superconducting ratio of the wire is 1.3. The sizes of cross-section of the bare wire and the insulated wire are 0.75 mm×1.20 mm and 0.83 mm×1.28 mm respectively, and the critical currents at 4.2 K and 5 T are both about 935 A.According to the size constraint of the magnet, we first calculate the current carrying zone of the superconducting coils and divide it into grid elements with parallel current. The size of each grid element is equal to that of the superconducting wire, and the distribution of non-rectangular coils is obtained by using 0-1 integer programming. In order to obtain a higher homogeneity of magnetic field, a reverse current zone is manually created in the wide blank area of the feasible current carrying zone. Using the results above, we then optimize the distribution of coils and build a rectangular model which facilitates the fabrication by using genetic algorithm. The inductance of the magnet is 1.8094 H, the operating current is 402.09 A, the stored energy is 146.27 kJ and the peak magnetic field of current carrying zone is 5.48 T. The calculated peak-to-peak homogeneity in 160 mm DSV is about 22 ppm. Taking into consideration the factors such as mechanical error and cold shrinkage, the estimated homogeneity would reach 60 ppm (peak-to-peak) with passive shimming.The 1.5 T extremity dedicated superconducting magnet is successfully fabricated through a series of processes such as winding, curing, assembly and welding. The prototype magnet has a room temperature bore of 280 mm in diameter and a total length of 520 mm, and the volume of liquid helium vessel is about 30 liters. To reduce the evaporation of liquid helium, a 1.5 Watt two-stage Gifford-McMahon refrigerator is employed to cool the system and maintain the evaporation rate of Helium at zero level. The range of 5 Gauss line of the magnet is 3.2 m in the radial direction and 2.6 m in the axial direction. Moreover, the magnet is magnetized to 1.5 T after being conditioned three times and the measured homogeneity in 160 mm DSV achieves 55 ppm (peak-to-peak) and 3.4 ppm (Vrms) after passive shimming using silicon steel pieces.