An elliptical climbing exercise apparatus includes a base frame, a swing unit including a pair of swing arms, a pedal unit including a pair of pedal shafts respectively pivotally connected to the swing arms, a damping unit including a rotating wheel with a spindle, a guiding unit including a pair of cranks respectively affixed to the two opposite ends of the spindle, a pair of rockers respectively pivotally connected to the cranks and a pair of links respectively pivotally connected to the rocker. Cooperation between the base frame, the swing unit, the pedal unit, the resistance unit and the guiding unit is used to achieve a training of the leg muscles.