Graphene and phosphorene are two major types of atomically thin two-dimensional materials under extensive investigation. However, the zero band gap of graphene and the instability of phosphorene greatly restrict their applications. Here, we make first-principle unbiased structure search calculations to identify a new buckled graphene-like PC6 monolayer with a number of desirable functional properties. The PC6 monolayer is a direct-gap semiconductor with a band gap of 0.84 eV, and it has an extremely high intrinsic conductivity with anisotropic character (i.e., its electron mobility is 2.94 x 10(5) cm(2) V-1 s(-1) along the armchair direction, whereas the hole mobility reaches 1.64 x 10(5) cm(2) V-1 s(-1) along the zigzag direction), which is comparable to that of graphene. On the other hand, PC6 shows a high absorption coefficient (10(5) cm(-1)) in a broad band, from 300 to 2000 nm. Additionally, its direct band gap character can remain within a biaxial strain of 5%. All these appealing properties make the predicted PC6 monolayer a promising candidate for applications in electronic and photovoltaic devices.