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In this paper, we study an atomic chain in the presence of modulated charge potential and modulated Rashba spin-orbit coupling (RSOC) of equal periods. We show that for commensurate periodicities, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#955;</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </semantics> </math> </inline-formula> with integer <i>n</i>, the three-dimensional synthetic space obtained by sliding the two phases of the charge potential and RSOC features a topological nodal-line semimetal protected by an anti-unitary particle-hole symmetry. The location and shape of the nodal lines strongly depend on the relative amplitude between the charge potential and RSOC.