Dual-stream constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a flexible waveform that can achieve low peak-to-average power ratio and high spectral efficiency. In this letter, a receiver with iterative detection based on amplitude-phase demodulator is proposed for the demodulation of the dual-stream CE-OFDM. Simulation results show that iterative detection with amplitude-phase demodulator outperforms the existing receiver for dual-stream CE-OFDM, especially for high phase-modulation index and high-order modulation constellation.