Magnetic resonance imaging (MRI) requires the gradient coils to produce magnetic field gradients, to encode three-dimensional information. In this work, a parametric method to the design of cylindrical transverse gradient coils for high-resolution magnetic resonance imaging (MRI) is proposed. The cylindrical transverse gradient coil was separated to several turns of curves, each turn is considered as a curve butted by two quasi-elliptic arcs. The parameterized curve is optimized with the simulated annealing algorithm. A cylindrical transverse gradient coil with high level of linearity is designed for 1.5 T MRI system. The cylindrical transverse gradient coil can build a high-quality transverse gradient magnetic field in a large spherical zone, concentric with the main magnet of the MRI system.