Analog radio-over-fiber (A-RoF) solutions for mobile fronthaul are regaining wide attention due to their high spectral efficiency and low complexity. However, the performance of A-RoF is usually limited by the fiber link fidelity. In this Letter, we propose and experimentally demonstrate an optical continuous pulse position modulation-based analog radio-over-fiber (OCPPM-RoF) scheme, in which the amplitudes of wireless waveforms are mapped to the time-domain positions of optical pulses to decouple the additive noise. The de-modulation of OCPPM-RoF signals is performed by a frequency-domain continuous position estimation (FD-CPE) algorithm including cross-power spectrum calculation and weighted least square for accurate delay estimation. In the experiment, by adopting appropriate pulse width factors, the recovered signal-to-noise ratio (SNR) can be flexibly adjusted within a wide range from 31.8 to 54.0 dB, supporting the transmission of various formats from 256-QAM to 65536-QAM. The results indicate that OCPPM-RoF can be a promising candidate for future fronthaul.