In this work, we present the synthesis, structure, and magnetic studies of three 1D homo-spin Dy(III) compounds in detail. For 1, one crystallography-independent Dy(III) site is contained and the coordination surrounding is a distorted square-antiprism geometry. Within 2, four crystallography-independent Dy(III) sites with largely distorted square-antiprism geometry are observed. As for 3, two crystallography-independent Dy(III) sites showing bicapped triangular-prism geometry are involved. The magnetic studies suggest weak ferromagnetic interactions for 1 and weak antiferromagnetic interactions for 2 and 3. Their dynamic magnetic properties are investigated by means of alternating current (ac) susceptibility measurement, revealing their slow magnetic relaxation. Moreover, a field-dependent ac signal is observed in 1, when by applying a static dc = 1000 Oe field, strong frequency-dependent ac signals and the peak of out-of-phase (χ'') can be clearly found. Ultimately, by fitting the Arrhenius law the energy barrier and relaxation time are estimated.