The paper proves the existence of impulsive periodic solutions of the first-order singular differential equation
where , , , and are continuous, 1-periodic functions. The nonlinearity is continuous in and 1-periodic in , , exist, and can have a singularity at . The model equation under interest is
where and is a real parameter. Impulses are continuous functions. In particular, they are linear homogeneous. The proof is based on a nonlinear alternative principle of Leray-Schauder and a truncation technique. Some recent results in the literature are generalized and improved.