This paper considers an energy-efficient transmit design in a general multiple-input single-output multiple-eavesdropper (MISOME) wiretap channel. Specifically, a transmitter sends one confidential message to a legitimate receiver, which must be kept perfectly secure from several external multi-antenna eavesdroppers. Assuming imperfect channel state information (CSI) at the transmitter, our goal is to design the input transmit covariance, such that the worst-case secrecy energy efficiency (WC-SEE) is maximized, subject to the quality of service (QoS) and total transmit power constraints. Due to the nonconvexity of this problem, an equivalent parametric reformulation, based on the fractional programming theory, is proposed to recast this problem as a sequence of semidefinite programs. By this means, the maximum WC-SEE can be found via a root search algorithm. Moreover, we also give an approach to constructing a rank-one optimal covariance matrix of the confidential message from our proposed algorithm, which implies the optimality of transmit beamforming to achieve the maximum WC-SEE. Numerical results are presented to verify the efficacy of our proposed method.