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Dual-functional radar communication (DFRC) is extremely attractive in the sixth generation systems, since it can simultaneously support communication and detection by a unified hardware platform with real-time cooperation. Considering the appealing features of multiple beams, this paper designs a dual mode multi-beam scheme composed of static and dynamic beams, so that it can simultaneously support multi-user transmission and high-accuracy targets detection. Besides, an integrated continuous phase modulation and linear frequency modulation signal is exploited to improve both range resolution of radar and bit error rate (BER) of users. To unify communication and radar systems, we define radar rate, and set the maximum sum-rate composed of communication and radar rates as the objective function. Since the optimization problem is non-convex, the problem is divided into two sub-issues, i.e., user selection, and joint beamforming design with power allocation. A successive maximum rate algorithm is presented for the former one, which can balance the performances between the sum-rate and complexity; and maximum minimization - Lagrange multiplier iteration algorithm is utilized to solve the latter one. In addition, some theoretical analyses, e.g., spectrum, BER, ambiguity function, false alarm and detection probabilities are deduced for the proposed system. Simulation results show that our proposed DFRC system can provide better sum-rate than the classical communication and radar separated systems.