We present passive mode locking of a vertical external-cavity surface-emitting laser (VECSEL) in the red spectral range with quantum dots (QDs) as active material in the gain and in the absorber structure. Both semiconductor samples are fabricated by metal-organic vapor-phase epitaxy (MOVPE) in a near-anti-resonant design. A v-shaped cavity is used to tightly focus onto the semiconductor saturable absorber mirror (SESAM), producing pulses with a duration of less than 1 ps and a repetition rate of 852MHz. In order to increase the field enhancement inside the absorber structure, some SESAM samples were additionally coated with a fused silica layer. The pulse duration as well as the mode locking stability were investigated for different thicknesses of the SiO2 layer. The most stable mode locking operation is observed for a 97 nm SiO2 layer, while the disadvantage of this overall near-resonant SESAM structure is an increased pulse duration of around 2 ps. Due to the improved stability, the transmission of the outcoupling mirror could be increased resulting in an average output power of 10 mW at an emission wavelength of 651 nm.