In this paper, we present a novel nonlinear control approach for underactuated crane systems with double-pendulum dynamics, which can achieve both rapid swing suppression and efficient cart positioning control. The controller has a simple structure which is easy for implementation, and it can increase the transient performance by introducing some coupling terms. Moreover, it shows satisfactory robustness w.r.t. parametric uncertainties. We provide rigorous Lyapunov-based stability analysis for the closed-loop system. To our knowledge, this paper yields the first closed-loop control scheme, without linearizing or approximating the dynamics, for crane systems with double-pendulum effects and uncertain/unknown parameters. At last, both numerical simulation and hardware experimental results are included to validate the effectiveness and feasibility of the proposed control scheme.