The temperature dependency of the dynamic Young's modulus and of the internal friction of La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF6428) was investigated by dynamic mechanical analysis. The significant decrease in the storage modulus of LSCF6428 with low oxygen vacancy concentration (LSCF1) and a following broad and asymmetric peak (P1) were interpreted as resulting from the motion of ferroelastic domain walls with a distribution of the relaxation time. The storage modulus of the LSCF6428 with higher oxygen vacancy concentration (LSCF2 and 3) was significantly larger than that of the LSCF1 at low temperatures. The P1 was barely observed with LSCF2 and 3. The increase in the storage modulus and the suppression of the peak P1 with increasing the oxygen vacancy concentration can be explained mainly by the pinning effect of the oxygen vacancies. This suggests that the oxygen vacancies play a vital role in determining the mobility of the ferroelastic domains in LSCF6428.