SSZ-13 zeolite (CHA structure) with small pore or 8-membered ring has been widely studied in catalysis and adsorption. Even SSZ-13 might be very useful in such applications, the synthesis usually relies on expensive organic templates. In this study, SSZ-13 was obtained, with a relatively inexpensive template, N,N,N-dimethylethylcyclohexylammonium bromide, from conversion of Y zeolites with wide silica/alumina ratios (SARs), especially in the absence of any crystal seed, additional silica and alumina. The obtained SSZ-13 s have relatively wide SAR of 6.9-36.7; and phase-pure SSZ-13 s could also be obtained from mixture of Y zeolites. The obtained SSZ-13 s, in proton form, were applied in ethylene-to-propylene (ETP) reaction, and the SSZ-13 with suitable SAR (18.8) had not only high propylene yield but also stable propylene production compared with other SSZ-13 s, showing the possible application of the SSZ-13 in ETP reaction.