Solid-state polymer-based electrolytes (SSPEs) exhibit great possibilities in realizing high-energy-density solid-state lithium metal batteries (SSLMBs). However, current SSPEs suffer from low ionic conductivity and unsatisfactory interfacial compatibility with metallic Li because of the high crystallinity of polymers and sluggish Li$^+$ movement in SSPEs. Herein, differing from common strategies of copolymerization, a new strategy of constructing a high-entropy SSPE from multivariant polymeric ligands is proposed. As a protocol, poly(vinylidene fluoride-co-hexafluoropropylene) (PH) chains are grafted to the demoed polyethylene imine (PEI) with abundant −NH$_2$ groups via a click-like reaction (HE-PEIgPHE). Compared to a PH-based SSPE, our HE-PEIgPHE shows a higher modulus (6.75 vs 5.18 MPa), a higher ionic conductivity (2.14 × 10$^{–4}$ vs 1.03 × 10$^{–4}$ S cm$^{–1}$), and a higher Li$^+$ transference number (0.55 vs 0.42). A Li|HE-PEIgPHE|Li cell exhibits a long lifetime (1500 h), and a Li|HE-PEIgPHE|LiFePO$_4$ cell delivers an initial capacity of 160 mAh g$^{–1}$ and a capacity retention of 98.7%, demonstrating the potential of our HE-PEIgPHE for the SSLMBs.