Si nanocrystals (Si-NCs) dispersible in polar liquid without surface functionalization by organic molecules have been realized by simultaneously doping n and p type impurities. We show that the codoped Si-NCs are stable in methanol for more than five months, while intrinsic Si-NCs prepared by the same procedure form large agglomerates. The different behavior of the intrinsic and codoped Si-NCs in solutions suggests that doped impurities exist on the surface of Si-NCs and the surface potential is large enough to prevent the agglomeration. The colloidal solution of codoped Si-NCs exhibits broad photoluminescence with the maximum in the near infrared range (1.1-1.3 eV).