In this paper, the successive cancellation (SC) heap polar decoding scheme is firstly proposed to reduce the complexity. Unlike SC list decoder which keeps $L$ same length paths, SC heap decoding stores different length paths in a heap and always decodes the global optimal path in the root. It has been strictly proved that SC heap decoding is superior to SC stack decoding because the time complexity of inserting new paths is only related to the height of the heap. Proposed SC heap decoding is a dynamic decoding scheme with robustness in various scenarios. Numerical results with binary-input additive white \emph{Gaussian} noise channel (BI- AWGNC) show that SC heap decoding reduces $63.53\%$ decoding complexity compared with SC list decoding on the same performance at SNR of $2.5$ dB. A low- complexity hardware architecture for proposed SC heap decoder is also designed.