Current　digital　watermarking　technologies　mainly　focus　on　the　imperceptibility　and　robustness　of　watermark　embedding,　while　the　security　of　watermarking　images　is　also　worth　further　research.　Considering　nonlinear　characteristics　and　the　integration　structure　of　storage　and　computation,　memristors　can　be　introduced　into　encryption　algorithms　to　improve　the　effect　of　encryption.　The　paper　proposes　a　double　encryption　algorithm　for　color　watermark　images　based　on　MCNN　(Memristive　Cellular　Neural　Networks)　and　Arnold　transform,　generates　chaotic　sequences　for　watermark　image　encryption　by　introducing　memristors　to　the　CNN　(Cellular　Neural　Networks)　to　construct　MCNN,　scrambles　the　images　using　the　Arnold　transform　to　achieve　the　double　encryption　of　pixel　values　and　pixel　positions,　and　enhances　the　security　of　the　watermark　images.　Adopting　the　SE　(Spectral　Entropy)　complexity　algorithm　optimizes　the　parameters　of　MCNN,　and　improves　the　performance　of　the　double　encryption　algorithm.　The　embedding　and　extraction　of　the　encrypted　watermark　image　is　realized　by　the　algorithm　combining　CT　(Contourlet　Transform)　and　SVD　(Singular　Value　Decomposition),　which　enhances　the　ability　to　resist　common　attacks　such　as　compression　and　rotation　attacks.　Experiment　results　show　the　proposed　algorithms　can　better　maintain　the　quality　of　the　color　watermark　images,　break　the　statistical　characteristics　of　the　original　images,　and　the　generated　key　has　good　randomness.　In　addition,　the　presented　algorithms　are　highly　sensitive　to　the　key,　and　improve　the　ability　to　resist　statistical　attacks,　differential　attacks,　exhaustive　attacks　and　common　image　attacks　with　good　security,　robustness　and　imperceptibility.　©　2024　IOP　Publishing　Ltd.　All　rights,　including　for　text　and　data　mining,　AI　training,　and　similar　technologies,　are　reserved.