Prediction of the fracture process in complex geometries needs special tools to take into account the highly non-linear behavior of both the fracture process and the error-prone mesh generation step. Taking this into account, one idea is to integrate phase-field modeling into the finite cell method (FCM). The phase-field approach aims to address the fracture process using a coupled problem where a continuous scalar variable, the so-called phase-field, will represent the crack. The FCM, on the other hand, is an immersed discretization technique wherein the complex physical geometry is embedded into a simple fictitious domain that can be meshed easily. With FCM, the aim is to simplify the mesh generation step of complex geometries which comes at a cost of higher complexity of the numerical integration. There are many integration schemes within the concept of FCM and the most popular among them are space-tree methods. The space-tree methods are very robust and applicable to almost all cases, but they are computationally expensive due to high number of integration points needed. This approach is way too expensive when it comes to the integration of phase-field FCM problems, where the number of elements must be very high at critical locations. Reducing the number of integration points reduces the accuracy and may cause instability or higher number of iterations within the phase-field solver. Moreover, in the most popular phase-field approach, we store the strain energy history at integration points and high number of integration points caused by employing space-tree approaches strongly affects the memory required. To avoid the above mentioned problems, we have employed the recently proposed non-negative moment fitting method (NNMF) approach which is introduced in [1] to solve phase-field FCM problems. With this method, the number of required integration points is much lower than the space-tree methods. The advantage of using this method will be shown and discussed. [1] W. Garhuom, A. Düster, Non-negative moment fitting quadrature for cut finite elements and cells undergoing large deformations, Computational Mechanics 70 (2022) 1059–1081.