Particles of non-spherical shape are always encountered in many real applications. In this work, we develop a new framework to directly simulate super-quadric (SQ) particles in fluid flows based on a forcing fictitious domain method. Specifically, a SQ function is used to represent the particle shape of different types in a flexible manner. Meanwhile, the immersion of particles in the fluid is handled by imposing rigid solid body motion in the particle domain, as well as adding a local forcing term to the Navier-Stokes equations by calculating the integral of both the pressure and the viscous forces over the whole particle domain. Particle shapes are varied by changing the five controlling parameters of the SQ equation. Furthermore, we validate our approach by performing simulations of flow around a fixed particle in 2D and 3D with different Reynolds numbers, as well as settling one sphere in 3D channels. The validation results indicate that the current simulation results show a good agreement with experimental data. Moreover, our method has been used to study the flow passing fixed ellipsoidal particles, and by comparing the results to reference show that the proposal method is found to be of comparable accuracy in predicting flow patterns and drag force, while being directly applicable to non-ellipsoid particle with Reynolds numbers between 0.1 and 3000. Also, the proposal approach has been used to study the flow around other SQ particle shape. The SQ particles exemplarily considered in the current study are an ellipsoidal particle and two fibre-like particles. We present the results for drag and lift coefficients of different shapes with a wide range of Reynolds numbers, as well as different particle orientations. The obtained results lay the foundation to apply the framework to flown through multi-particle systems in the near future. (C) 2019 Elsevier B.V. All rights reserved.