Abstract: The conditional nonlinear optimal perturbation (CNOP) is a new theoretical method proposed by Mu，et al in 2003, which is an extension of the linear singular vector (LSV) to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system. However, the wide application of this method has been limited due to its large computational cost caused by the use of adjoint technique in its solution. In order to greatly reduce the computational cost of the solution to CNOP, we propose a fast algorithm for it based on empirical orthogonal function (EOF). The algorithm is preliminarily tested in a target observation experiment of the typhoon “Matsa” using the Global and Regional Assimilation Prediction System (GRAPES), a regional operational forecast model. The effectivity and feasibility of the algorithm to determine the sensitive (targeting) area in target observation is evaluated through an observing system simulation experiment (OSSE). The results from the OSSE show that the energy of the CNOP obtained by the new algorithm develops quickly and nonlinearly. In the experiment of target observation of the typhoon “Matsa”, the sensitivity area is effectively identified using the CNOP obtained from the new method with 24 hours as the prediction time length, and the 24 h accumulated rainfall prediction errors in the verification area are reduced significantly comparing with the “true states” when the initial conditions in the sensitivity area are replaced by the “observations”. Especially, the decrease of accumulated rainfall prediction errors can be extended to longer time (e.g. 72 hour), although the verification is just at the time 24 hours after the initial time. Further analyses reveal that the decrease of 24 h accumulated rainfall prediction errors in the verification area benefits from the improvements of initial structure of warm core of typhoon, upper-layer relative vorticity, water vapor conditions and so on due to the update of the initial conditions in the sensitivity area.