Palette images are widely used in multimedia and Internet applications. In this paper, a new method for data hiding in palette images with security protection by color ordering and mapping, as well as parameter randomization, is proposed. First, image pixels are classified as data embeddable or nonembeddable, and only the former ones are used to embed secret data. The proposed idea of data hiding is based on the use of a new type of color-ordering relationship, from which a color-mapping function is defined with binary values as output. When a secret data bit is to be embedded, a data-embeddable pixel is selected, and its color is adjusted to make the output of the color-mapping function equal to the secret bit value. The embedded secret data can be extracted correctly and quickly from the resulting stego-image by merely inspecting the outputs of the color-mapping function. Indetectability of the secret information embedded by the proposed method is also analyzed and confirmed. Furthermore, a number of possible security enhancement measures based on parameter randomization in the data-embedding process are proposed to protect the hidden data in the stego-image. The randomization effect is created by the use of a secret key and a number of random number-generating functions. The proposed data hiding method was tested with a variety of palette images. The experimental results show that secret data can be embedded and extracted successfully without producing visual artifacts in the cover image. A good balance between stego-image quality and data-embedding capacity can be achieved, which proves the efficiency and feasibility of the proposed method for practical applications.