SrFeF5 is a typical spin-chain compound with strong intrachain and moderate interchain interactions. It has been predicted to be multiferroic due to the cycloidal spin structure. Herein, we provide clear experimental evidence of multiferroicity of SrFeF5 by a systematic investigation of its magnetic, dielectric, and pyroelectric properties. The complicated interactions between neighboring Fe ions lead to the following three magnetic transitions. The divergence between field cooling (FC) and zero field cooling (ZFC) M(T) curves at TN1∼ 80 K originates from the antiparallel alignment of neighboring spins along the chains due to the strong intrachain interactions. The sudden increase in magnetization with further divergence between the FC and ZFC M(T) curves is observed at TN2 ∼ 42 K, which originates from the formation of cycloidal spin structure due to the contribution from moderate interchain interactions. An upturn of magnetization with further decreasing temperature at TN3 ∼ 6 K is due to the contribution from the much weaker interchain interactions. Exchange bias starts to emerge at around 30 K, reaches a maximum at 20 K, and further increases below 10 K. A frequency independent peak of dielectric constant is observed at around TN2, due to the cycloidal spin structure induced spontaneous polarization. This work helps to understand the multiferroic properties in the spin-chain fluorides.