Are you using RI detector ? if yes , use mobile phase with lower refractive index than solute.
The other thing you can do is try to dissolve sample in mobile phase and changing the polarity of the mobile phase will help in overcoming negative peaks. .Also check blank (mobile phase ) if it has too much UV absorption ,Either change UV wavelength or change mobile phase that has less absorption than solute.
I have observed this for fungal extracts with compounds that absorb at the reference wavelength. I suggest that you look at the DAD spectrum of your negative peaks and that you try to adjust the reference wavelength. (I assume that your chromatogram does not show negative peaks when you inject a blank sample.)
Be aware that if you decide to work with reference wavelength off, your baseline will most probably be not horizontal. You can circumvent that by subtracting the baseline of a blank sample after the analysis.
Negative peak could be due to the less absorbance of the analyte than mobile phase or due to disturbance in the equilibrium of mobile phase when it passes through column after injection. If you are using RID then its quite normal. If you are using PDA or UVD then you can try solvent with lower or almost equivalent absorbance as that of analyte. Furthermore, thoroughly check the ferrule attached to inlet of column if it is loose then some air might interfere and lead to negative peak. Also properly filter and sonicate your solvents before use.
Negative peaks may appear when there is a mismatch between the mobile phase and the solvent used to prepare the sample especially when the solvent is acidic. Negative peaks may also be due to impurities in the mobile phase having a higher concentration than impurities found in the sample. Check the compatibility of the extraction solvent used sample preparation and the mobile phase. Also, check the level of impurity of the mobile phase
Hi Gloria: The most common reason for negative HPLC peaks seen with a diode array detector is that you have turned 'ON' the Reference Wavelength feature! Please, turn this feature 'OFF' unless you want the computer to automatically destroy raw data and make your method out-of-compliance and invalid. Please read this article for a better understanding of this problem. "REFERENCE WAVELENGTHS (as used in HPLC UV/VIS): " http://hplctips.blogspot.com/2011/03/reference-wavelengths-as-used-in-hplc.html
This second article may also be of interest too: "Proper Wavelength Selection for HPLC Method Development (or Purity Determination)" http://hplctips.blogspot.com/2013/08/wavelength-selection-for-method.html