Chaotic systems are an effective tool for various applications, including information security and internet of things. Many chaotic systems may have the weaknesses of incomplete output distributions, discontinuous chaotic regions, and simple chaotic behaviors. These may result in many negative influences in practical applications utilizing chaos. To deal with these issues, this study introduces a modular chaotification model (MCM) to increase the dynamic properties of current one-dimensional (1D) chaotic maps. To exhibit the effect of the MCM, three 1D chaotic maps are improved using the MCM as examples. Studies of the resulting properties show the robust and complex dynamics of these improved chaotic maps. Moreover, we implement these improved chaotic maps of MCM in a field-programmable gate array hardware platform and apply them to the application of PRNG. Performance analyses verify that these chaotic maps improved by the MCM have more complicated chaotic behaviors and wider chaotic ranges than the existing and several new chaotic maps.