It is well known that a graph $G$ has a symmetric spectrum if and only if it is bipartite, a signed graph $Γ=(G,σ)$ has a symmetric spectrum if $G$ is bipartite. However, there exists a spectrally symmetric signed graph $Γ=(G,σ)$ such that $G$ is not bipartite. In this paper, we focus to characterize the signed graphs with symmetric spectra. Some necessary and (or) sufficient conditions for spectrally symmetric signed graphs are given. Moreover, some methods to construct signed graphs with symmetric spectra are found and infinite families of these signed graphs are produced.