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We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^p\left(𝒳\right)$ for $1/(1+ϵ)<p\le 1$, where $𝒳$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $ϵ$ is the regularity exponent of the kernel of the singular integral operator $T$. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón’s identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was...