High frequency magnetic precessions with strong intensity are strongly desired in material systems for high performance magnetic memory or nano-oscillator applications with ultrafast manipulation speed. Here, we demonstrate an exchange-coupled asymmetric composite film structure of Ta/Pd/[Pd/Co]5/Cu(tCu)/[Co/Ni]5/Ta with adjustable strong perpendicular magnetic anisotropy and interlayer coupling strength, in which the dynamic magnetic properties are systematically studied by using time-resolved magneto-optical Kerr effect spectroscopy. It is demonstrated that the in-phase precession frequency is between those of the single hard magnetic [Pd/Co]5 and soft [Co/Ni]5 multilayers, which can be significantly enhanced for the strongly coupled case at tCu < 1 nm. Moreover, in the weakly coupled samples with tCu = 1.0-3.0 nm, besides the common in-phase acoustic mode, an out-of-phase optical mode occurs simultaneously with a frequency even higher than that of the hard magnetic [Pd/Co]5 layer. The optical mode precession frequency and amplitude show an unusual non-monotonic variation trend with the increase of tCu, which has been theoretically analyzed and attributed to the co-effect of decreased coupling strength and increased magnetic anisotropy field difference between the two multilayer stacks. Moreover, by adjusting tCu and the [Co/Ni] repetition number N, an optical mode of strong intensity can be actively achieved, even reaching 80% as compared to the acoustic mode. These results provide effective control and better understanding of magnetic dynamics in perpendicular composite films, which are of key importance for developing ultrafast spintronics-based devices.