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We derive an exact solution for a spherically symmetric Bardeen black hole surrounded by perfect fluid dark matter (PFDM).By treating the magnetic charge g and dark matter parameter α as thermodynamic variables,we find that the first law of thermodynamics and the corresponding Smarr formula are satisfied.The thermodynamic stability of the black hole is also studied.The results show that there exists a critical radius r+C where the heat capacity diverges,suggesting that the black hole is thermodynamically stable in the range 0 ＜ r+ ＜ r+C.In addition,the critical radius r+C increases with the magnetic charge g and decreases with the dark matter parameter α.Applying the Newman-Janis algorithm,we generalize the spherically symmetric solution to the corresponding rotating black hole.With the metric at hand,the horizons and ergospheres are studied.It turns out that for a fixed dark matter parameter α,in a certain range,with the increase of the rotation parameter a and magnetic charge g,the Cauchy horizon radius increases while the event horizon radius decreases.Finally,we investigate the energy extraction by the Penrose process in a rotating Bardeen black hole surrounded by PFDM.