We consider the generalized Gagliardo-Nirenberg inequality in \(\Bbb{R}^{n}\) including homogeneous Besov space \(\dot{B}^{s}_{r,\rho}(\Bbb{R}^{n})\) with the critical order s=n/r, which describes the continuous embedding such as \(L^{p}(\Bbb{R}^{n})\cap\dot{B}^{n/r}_{r,\rho}(\Bbb{R}^{n})\subset L^{q}(\Bbb{R}^{n})\) for all q with p≦q<∞, where 1≦p≦r<∞ and 1<ρ≦∞. Indeed, the following inequality holds: $$\|u\|_{L^{q}(\Bbb{R}^{n})}\leqq C\,q^{1-1/\rho}\|u\|_{L^{p}(\Bbb{R}^{n})}^{p/q}\|u\|_{\dot{B}^{n/r}_{r,\rho}(\Bbb{R}^{n})}^{1-p/q},$$ where C is a constant depending only on r. In this inequality, we have the exact order 1−1/ρ of divergence to the power q tending to the infinity. Furthermore, as a corollary of this inequality, we obtain the Gagliardo-Nirenberg inequality with the homogeneous Triebel-Lizorkin space \(\dot{F}^{n/r}_{r,\rho}(\Bbb{R}^{n})\) , which implies the usual Sobolev imbedding with the critical Sobolev space \(\dot{H}^{n/r}_{r}(\Bbb{R}^{n})\) . Moreover, as another corollary, we shall prove the Trudinger-Moser type inequality in \(\dot{B}^{n/r}_{r,\rho}(\Bbb{R}^{n})\) .