GFSPX is a lightweight block cipher proposed by Zhang et al. in 2024, aiming to provide sufficient security for devices in resource-constrained environments. In this paper, we first give the impossible differential cryptanalysis against 5-round and 6-round GFSPX. Firstly, we investigate the round of GFSPX to get full diffusion under encryption and decryption respectively, as well as the properties of its component functions. Secondly, we construct the 4-round, 5-round and 6-round impossible differential distinguishers against GFSPX based on the properties of the component functions. At last, using the 4-round impossible differential distinguisher, the key recovery attacks against the 5-round and 6-round GFSPX are constructed. The data complexity is ${{2}^{22}}$ and time complexity is ${{2}^{68}}$ 5-round encryption against 5-round key recovery attack. The data complexity is ${{2}^{56}}$ and time complexity is ${{2}^{117.4}}$ 6-round encryption against 6-round key recovery attack.