The generalized variable-coefficient Burgers-Kadomtsev-Petviashvili (BKP) equation was investigated employing the Painleve analysis technique. It showed that the equation does not possess the Painleve property. Via the truncated Painleve expansion method and under the condition f(t)=cg(t) (c is a constant), an auto-Bcklund transformation for the generalized variable-coefficient Burgers-Kadomtsev-Petviashvili equation was derived. Based on the obtained auto-Bcklund transformation, some novel exact analytic solutions were given, including multiple soliton and periodic solutions.