Non-invasive optical focusing inside scattering media is still a big challenge because inhomogeneous media scatter both incoming photons for focusing and outgoing photons for observation. Various approaches, utilizing non-linear fluorescence or ultrasound, have been reported to address this difficulty. However, implementation of these methods is complicated and highly expensive, as ultrafast laser systems or photo-acoustic equipment must be employed. Here, we demonstrate a wavefront shaping technique to achieve non-invasive focusing (NiF) inside scattering media using only a linear fluorescent signal. Contrast and mean of incoherent speckles, produced by the linear fluorescence, are utilized as feedback signals to optimize the input wavefront. While increasing speckle contrast makes the focus tighter, and increasing the speckle mean enhances the intensity, fine-tuning the contribution of these two factors in our two-step optimization is essential. An optimal wavefront is found to achieve simultaneously both a micrometer focal spot size (down to 20 um diameter) and high intensity (more than a 100-fold enhancement) inside the scattering media. Our method promises a new route in life science towards focusing, imaging or manipulating deep into biological tissues with linear fluorescent agents.