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In this work, we present two linearly and unconditionally energy stable numerical schemes for a vesicle membrane model that exactly satisfies the conservation of volume constraint and penalizes the surface area constraint. First of all, we introduce some auxiliary variables to transform the original model into an equivalent system using the energy quadratization(EQ) technique. Moreover, with the transformed free energy a quadratic functional with respect to the new variables and the modified energy dissipative law is satisfied. Then an implicit-explicit(IMEX) time discrete technique for the semi-discrete scheme is used to construct two linearly and unconditionally energy stable fully discrete schemes for the model. Finally, numerical experiments are presented to demonstrate the accuracy and unconditionally energy-stability of the proposed schemes. [ABSTRACT FROM AUTHOR]