This work obtains the efficiency at maximum power for a stochastic heat engine performing Carnot-like, Stirling-like and Ericsson-like cycles. For the mesoscopic engine a Brownian particle trapped by an optical tweezers is considered. The dynamics of this stochastic engine is described as an overdamped Langevin equation with a harmonic potential, whereas is in contact with two thermal baths at different temperatures, namely, hot (T h ) and cold (T c ). The harmonic oscillator Langevin equation is transformed into a macroscopic equation associated with the mean value x 2 (t) using the original Langevin approach. At equilibrium stationary state this quantity satisfies a state-like equation from which the thermodynamic properties are calculated. To obtained the efficiency at maximum power it is considered the finite-time cycle processes under the framework of low dissipation approach.