In this paper, we investigate a delayed Nicholson equation with delay harvesting term which was proposed in open problems and conjectures formulated by Berezansky et al. (Applied Mathematical Modelling 34 (2010) 1405). The stability switching curves by taking two delays as parameters are obtained via the method introduced by An et al.(J. Differential Equations 266 (2019) 7073). The existence of Hopf singularity on a two-parameter plane is determined by the varying direction of two parameters. Furthermore, the normal form near the Hopf singularity is derived via applying the center manifolds theory and normal forms method of FDEs. Finally, some numerical simulations are carried out to illustrate the theoretical conclusions.