We present passive mode locking of a vertical external-cavity surface-emitting laser (VECSEL) in the red spectral range. The gain structure includes 20 compressively strained GaInP quantum wells (QWs), which are arranged in a resonant periodic gain design containing five packages of four quantum wells each. We use tensile strained AlGaInP barriers and cladding layers to compensate the strain introduced by the quantum wells. The semiconductor saturable absorber mirror (SESAM) includes two of the same quantum wells as used in the gain structure, positioned close to the surface. The semiconductor structure is grown by MOVPE in a near-resonant design and coated with a fused silica layer for an overall anti-resonant design. For tight focussing of the laser mode onto the absorber, we use a v-shaped cavity with an overall length of 179mm. Autocorrelation measurements show a FWHM pulse duration below 250 fs with side pulses arising due to the diamond heatspreader bonded onto the gain chip. The laser spectrum consists of a soliton-like part at 664.5 nm and a "continuum" which is also found in autocorrelation measurements perfomed in a Hanbury-Brown and Twiss type setup. An FFT based frequency analysis of the emitted pulse train shows a repetition rate of 836MHz. The SESAM charge carrier dynamics were investigated by pump-probe measurements. We observe a tri-exponential decay with a dominant fast decay time in the range of the pulse duration.