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A 70 MeV cyclotron for radioactive ion beam production and other applications has been designed at China Institute of Atomic Energy (CIAE). The main challenge of the magnet design for this particle machine lies in the needs of two isochronous magnetic fields to accelerate H- and D- with charge-mass ratios of 1 and 0.5 respectively. The required isochronisms are achieved by installing removable shims and adjusting the RF frequency. The magnetic fields and beam dynamics design results for both H- and D- beams are described in this paper. The analysis on field imperfections caused by the magnet deformation and the effects of annealing on magnetic properties of materials, are also outlined.