By constructing an odd function with multiple piecewise-linear segments in the double-folded torus chaotic attractor equation and using recurrence algorithm, the recurrence formula capable of producing a family of multi-folded torus chaotic attractors is derived. Utilizing the recurrence formula thus derived and selecting properly the slope values of piecewise-linear segments, the values for equilibrium points and breakpoints are calculated. Eventually, a family of multiple-folded torus chaotic attractors can be obtained. Results of numeral simulations by using computer for generating this kind of chaotic attractors are also given.