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A new ephemeris, period change analysis and light curve modeling of the W UMa-type eclipsing binary BF Pav are presented in this study. Light curves of the system taken in BVRI filters from two observatories in Australia and Argentina were modeled using the Wilson-Devinney code. The results of this analysis demonstrate that BF Pav is a contact binary system with a photometric mass ratio q=1.460+_0.014, a fillout factor f=12.5%, an inclination of 87.97+_0.45 deg and a cold spot on the secondary component. By using the distance modulus formula, the distance of BF Pav was calculated to be d=268+_18 pc which is in good agreement with the Gaia EDR3 distance. We obtain an orbital period increase at a rate of 0.142 s/century due to a quadratic trend in the O-C diagram. Also, an alternative sudden period jump probably has occurred which could be interpreted as a rapid mass transfer from the lower mass star to its companion about DeltaM=2.45*10^(-6) Msun. Furthermore, there is an oscillatory behavior with a period of 18.3+_0.3 yr. Since BF Pav does not seem to have significant magnetic activity, this behavior could be interpreted as the light-time effect caused by an undetected third body in this system. In this case, the probability for the third body to be a low mass star with M>=0.075 Msun or a brown dwarf is 5.4% and 94.6% respectively. If we assume i'=90deg, a_3=8.04+_0.33 AU. The mass of the secondary component was also determined using two different methods which result close to each other.