In this paper, a joint beamforming design for max-min fair simultaneous wireless information and power transfer (SWIPT) is investigated in a green cloud radio access network (Cloud-RAN) with millimeter wave (mmWave) wireless fronthaul. To achieve a balanced user experience for separately located data receivers (DRs) and energy receivers (ERs) in the network, joint transmit beamforming vectors are optimized to maximize the minimum data rate among all the DRs, while satisfying each ER with sufficient RF energy at the same time. Then, a two-step iterative algorithm is proposed to solve the original non-convex optimization problem with the fronthaul capacity constraint in an $l_0$-norm form. Specifically, the $l_0$-norm constraint can be approximated by the reweighted $l_1$-norm, from which the optimal max-min data rate and the corresponding joint beamforming vector can be derived via semidefinite relaxation (SDR) and bi-section search. Finally, extensive numerical simulations are performed to verify the superiority of the proposed joint beamforming design to other separate beamforming strategies.