The isomerization of cycloalkenes via the formation of carbenium cations assisted by the Brønsted acid site (BAS) in zeolites is the vital reaction step in hydrocracking and hydroisomerization processes of the petrochemical industry. To understand the acid-catalyzed positional isomerization and skeletal isomerization of cycloalkenes via carbenium intermediates, a series of ab initio molecular dynamics (AIMD) simulations of cyclohexene within the H-BEA zeolite have been carried out. AIMD simulations combined with the enhanced sampling technique reveal that the half-chair conformer is the most stable conformation for cyclohexene within H-BEA. Free energy landscapes characterizing protonation/deprotonation, positional isomerization, and skeletal isomerization of cyclohexene have been mapped out at 413 K. The free energy barrier for the formation of carbenium is calculated to be 44 kJ mol-1. The skeletal isomerization of cyclohexene to methylcyclopentylium via the protonated cyclopropane transition state involves four stages with a total free energy barrier of 134 kJ mol-1. Further geometrical analysis provides additional information about the structural origin of free energy barriers.